Future Value of Given present value calculate future value

Document Sample
Future Value of Given present value calculate future value Powered By Docstoc
					                                            Future Value of $1
                                 Given present value calculate future value
       3%       4%       5%       6%      7%       8%      9%      10%      11%      12%       13%       14%
 1   1.030    1.040    1.050    1.060 1.070 1.080 1.090 1.100 1.110                 1.120     1.130     1.140
 2   1.061    1.082    1.103    1.124 1.145 1.166 1.188 1.210 1.232                 1.254     1.277     1.300
 3   1.093    1.125    1.158    1.191 1.225 1.260 1.295 1.331 1.368                 1.405     1.443     1.482
 4   1.126    1.170    1.216    1.262 1.311 1.360 1.412 1.464 1.518                 1.574     1.630     1.689
 5   1.159    1.217    1.276    1.338 1.403 1.469 1.539 1.611 1.685                 1.762     1.842     1.925
 6   1.194    1.265    1.340    1.419 1.501 1.587 1.677 1.772 1.870                 1.974     2.082     2.195
 7   1.230    1.316    1.407    1.504 1.606 1.714 1.828 1.949 2.076                 2.211     2.353     2.502
 8   1.267    1.369    1.477    1.594 1.718 1.851 1.993 2.144 2.305                 2.476     2.658     2.853
 9   1.305    1.423    1.551    1.689 1.838 1.999 2.172 2.358 2.558                 2.773     3.004     3.252
10   1.344    1.480    1.629    1.791 1.967 2.159 2.367 2.594 2.839                 3.106     3.395     3.707
11   1.384    1.539    1.710    1.898 2.105 2.332 2.580 2.853 3.152                 3.479     3.836     4.226
12   1.426    1.601    1.796    2.012 2.252 2.518 2.813 3.138 3.498                 3.896     4.335     4.818
13   1.469    1.665    1.886    2.133 2.410 2.720 3.066 3.452 3.883                 4.363     4.898     5.492
14   1.513    1.732    1.980    2.261 2.579 2.937 3.342 3.797 4.310                 4.887     5.535     6.261
15   1.558    1.801    2.079    2.397 2.759 3.172 3.642 4.177 4.785                 5.474     6.254     7.138
16   1.605    1.873    2.183    2.540 2.952 3.426 3.970 4.595 5.311                 6.130     7.067     8.137
17   1.653    1.948    2.292    2.693 3.159 3.700 4.328 5.054 5.895                 6.866     7.986     9.276
18   1.702    2.026    2.407    2.854 3.380 3.996 4.717 5.560 6.544                 7.690     9.024    10.575
19   1.754    2.107    2.527    3.026 3.617 4.316 5.142 6.116 7.263                 8.613    10.197    12.056
20   1.806    2.191    2.653    3.207 3.870 4.661 5.604 6.727 8.062                 9.646    11.523    13.743

                                          Future Value of Annuity of $1
                                       Given annuity calculate future value
        3%       4%       5%        6%       7%       8%         9%      10%        11%       12%       13%       14%
 1    1.000    1.000    1.000     1.000    1.000    1.000     1.000     1.000      1.000     1.000     1.000     1.000
 2    2.030    2.040    2.050     2.060    2.070    2.080     2.090     2.100      2.110     2.120     2.130     2.140
 3    3.091    3.122    3.153     3.184    3.215    3.246     3.278     3.310      3.342     3.374     3.407     3.440
 4    4.184    4.246    4.310     4.375    4.440    4.506     4.573     4.641      4.710     4.779     4.850     4.921
 5    5.309    5.416    5.526     5.637    5.751    5.867     5.985     6.105      6.228     6.353     6.480     6.610
 6    6.468    6.633    6.802     6.975    7.153    7.336     7.523     7.716      7.913     8.115     8.323     8.536
 7    7.662    7.898    8.142     8.394    8.654    8.923     9.200     9.487      9.783    10.089    10.405    10.730
 8    8.892    9.214    9.549     9.897 10.260 10.637 11.028 11.436               11.859    12.300    12.757    13.233
 9   10.159   10.583   11.027    11.491 11.978 12.488 13.021 13.579               14.164    14.776    15.416    16.085
10   11.464   12.006   12.578    13.181 13.816 14.487 15.193 15.937               16.722    17.549    18.420    19.337
11   12.808   13.486   14.207    14.972 15.784 16.645 17.560 18.531               19.561    20.655    21.814    23.045
12   14.192   15.026   15.917    16.870 17.888 18.977 20.141 21.384               22.713    24.133    25.650    27.271
13   15.618   16.627   17.713    18.882 20.141 21.495 22.953 24.523               26.212    28.029    29.985    32.089
14   17.086   18.292   19.599    21.015 22.550 24.215 26.019 27.975               30.095    32.393    34.883    37.581
15   18.599   20.024   21.579    23.276 25.129 27.152 29.361 31.772               34.405    37.280    40.417    43.842
16   20.157   21.825   23.657    25.673 27.888 30.324 33.003 35.950               39.190    42.753    46.672    50.980
17   21.762   23.698   25.840    28.213 30.840 33.750 36.974 40.545               44.501    48.884    53.739    59.118
18   23.414   25.645   28.132    30.906 33.999 37.450 41.301 45.599               50.396    55.750    61.725    68.394
19   25.117   27.671   30.539    33.760 37.379 41.446 46.018 51.159               56.939    63.440    70.749    78.969
20   26.870   29.778   33.066    36.786 40.995 45.762 51.160 57.275               64.203    72.052    80.947    91.025



                                           Page 1 of 27
                                          Present Value of $1
          Given future value calculate present value (How much of future amount is principal)
       3%      4%       5%       6%      7%       8%      9%    10%      11%     12%       13%    14%
 1   0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885                           0.877
 2   0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783                           0.769
 3   0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693                           0.675
 4   0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613                           0.592
 5   0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543                           0.519
 6   0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480                           0.456
 7   0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425                           0.400
 8   0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376                           0.351
 9   0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333                           0.308
10   0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295                           0.270
11   0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261                           0.237
12   0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231                           0.208
13   0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204                           0.182
14   0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181                           0.160
15   0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160                           0.140
16   0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 0.141                           0.123
17   0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125                           0.108
18   0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111                           0.095
19   0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098                           0.083
20   0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087                           0.073

                                      Present Value of Annuity of $1
                 Given annuity calculate present value (calculate equivalent amount today)
        3%       4%       5%       6%        7%       8%       9%     10%     11%     12%     13%     14%
 1    0.971    0.962    0.952    0.943     0.935 0.926 0.917 0.909 0.901 0.893               0.885   0.877
 2    1.913    1.886    1.859    1.833     1.808 1.783 1.759 1.736 1.713 1.690               1.668   1.647
 3    2.829    2.775    2.723    2.673     2.624 2.577 2.531 2.487 2.444 2.402               2.361   2.322
 4    3.717    3.630    3.546    3.465     3.387 3.312 3.240 3.170 3.102 3.037               2.974   2.914
 5    4.580    4.452    4.329    4.212     4.100 3.993 3.890 3.791 3.696 3.605               3.517   3.433
 6    5.417    5.242    5.076    4.917     4.767 4.623 4.486 4.355 4.231 4.111               3.998   3.889
 7    6.230    6.002    5.786    5.582     5.389 5.206 5.033 4.868 4.712 4.564               4.423   4.288
 8    7.020    6.733    6.463    6.210     5.971 5.747 5.535 5.335 5.146 4.968               4.799   4.639
 9    7.786    7.435    7.108    6.802     6.515 6.247 5.995 5.759 5.537 5.328               5.132   4.946
10    8.530    8.111    7.722    7.360     7.024 6.710 6.418 6.145 5.889 5.650               5.426   5.216
11    9.253    8.760    8.306    7.887     7.499 7.139 6.805 6.495 6.207 5.938               5.687   5.453
12    9.954    9.385    8.863    8.384     7.943 7.536 7.161 6.814 6.492 6.194               5.918   5.660
13   10.635    9.986    9.394    8.853     8.358 7.904 7.487 7.103 6.750 6.424               6.122   5.842
14   11.296   10.563    9.899    9.295     8.745 8.244 7.786 7.367 6.982 6.628               6.302   6.002
15   11.938   11.118 10.380      9.712     9.108 8.559 8.061 7.606 7.191 6.811               6.462   6.142
16   12.561   11.652 10.838 10.106         9.447 8.851 8.313 7.824 7.379 6.974               6.604   6.265
17   13.166   12.166 11.274 10.477         9.763 9.122 8.544 8.022 7.549 7.120               6.729   6.373
18   13.754   12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250                      6.840   6.467
19   14.324   13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366                      6.938   6.550
20   14.877   13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469                      7.025   6.623



                                         Page 2 of 27
Problem 2.1

                            Future Value of $1
               Given present value calculate future value
Caspian Corporation invested $4,000 in a savings account that earned
10% interest compounded semi-annually. At the end of three years
Caspian withdrew the principal and interest. Prepare the
accumulation schedule for the first six periods (3 years).
Given:    Present value (PV)                                   $4,000
           Interest rate per year (R)                           10%
           Years of investment (Y)                                 3
           Compounding periods per year (c)                        2
Calculate: Interest rate per period (i = R / c)                  5%
           Number of periods (n = Y × c)                           6
           Future value of $1 factor                           1.340
Calculate future value using tables {calculator}              $5,360
                                        A × R × 1/c =         A + B=
                          (A)                  A×i=               (C)
                   Beginning                      (B)         Ending
                     Balance                 Interest        Balance
     1                 4,000                     200           4,200
     2                  4,200                     210          4,410
     3                  4,410                     221          4,631
     4                  4,631                     232          4,863
     5                  4,863                     243          5,106
     6                  5,106                     254          5,360




                                Page 3 of 27
Problem 2.2

                          Future Value of $1
              Given present value calculate future value
You deposited $14,000 in a savings account at a bank. The account
paid interest at the rate of 16% compounded quarterly. Prepare the
accumulation schedule for the first six periods (1.5 years).
Given:     Present value (PV)
                                                                $14,000
           Interest rate per year (R)
                                                                   16%
           Years of investment (Y)
                                                                     1.5
           Compounding periods per year (c)
                                                                       4
Calculate: Interest rate per period (i = R / c)
                                                                    4%
           Number of periods (n = Y × c)
                                                                       6
           Future value of $1 factor
                                                                  1.265
Calculate future value using tables {calculator}
                                                       $17,710 {17,714}
                                       A × R × 1/c =             A + B=
                           (A)                 A×i=                  (C)
                   Beginning                      (B)            Ending
                      Balance                Interest           Balance
      1
                14,000                  560                14,560
      2
                14,560                  582                15,142
      3
                15,142                  606                15,748
      4
                15,748                  630                16,378
      5
                16,378                  655                17,033
      6
                17,033                  681                17,714




                             Page 4 of 27
Problem 3.1

                          Present Value of $1
              Given future value calculate present value
Pacific Corporation needs $100,000 at the end of six years. If Pacific
could earn 14% compounded annually, how much would it need to
invest today.
Given:     Future value (FV)                                   $100,000
           Interest rate per year (R)                             14%
           Years of investment (Y)                                   6
           Compounding periods per year (c)                          1
Calculate: Interest rate per period (i = R / c)                   14%
           Number of periods (n = Y × c)                             6
           Present value of $1 factor                            0.456
Calculate present value using tables {calculator}       45,600 {45,559}
                                        A × R × 1/c =          A + B=
                         (A)                   A×i=                (C)
                  Beginning                       (B)          Ending
                    Balance                  Interest         Balance
     1               45,600                     6,384          51,984
     2                51,984                   7,278            59,262
     3                59,262                   8,297            67,559
     4                67,559                   9,458            77,017
     5                77,017                  10,782            87,799
     6                87,799                  12,201           100,000




                               Page 5 of 27
Problem 3.2

                           Present Value of $1
               Given future value calculate present value
Assume you want $30,000 at the end of three years. If you could earn
16% compounded semi-annually, how much would you need to invest
today?
Given:     Future value (FV)
                                                                $30,000
           Interest rate per year (R)
                                                                   16%
           Years of investment (Y)
                                                                       3
           Compounding periods per year (c)
                                                                       2
Calculate: Interest rate per period (i = R / c)
                                                                    8%
           Number of periods (n = Y × c)
                                                                       6
           Present value of $1 factor
                                                                  0.630
Calculate present value using tables {calculator}
                                                        18,900 {18,905}
                                       A × R × 1/c =             A + B=
                          (A)                  A×i=                  (C)
                  Beginning                       (B)           Ending
                     Balance                 Interest          Balance
     1
               18,900                  1,512              20,412
     2
               20,412                  1,633              22,045
     3
               22,045                  1,764              23,809
     4
               23,809                  1,905              25,714
     5
               25,714                  2,057              27,771
     6
               27,771                  2,222              29,993




                             Page 6 of 27
Problem 6.1

                      Future Value of Annuity of $1
                  Given annuity calculate future value
Baltic Corporation deposited $10,000 at the end of each six months
into a savings account that earns an annual rate of interest of 8%,
compounded semi-annually. How much will investments grow to at
the end of 3 years?
Given:     Annuity [also called PMT]                             $10,000
           Interest rate per year (R)                                8%
           Years of investment (Y)                                     3
           Payment/compounding periods per year (c)                    2
           Payment at end of period

Calculate: Interest rate per period (i = R / c)                     4%

            Number of periods (n = Y × c)                             6

            Future value of annuity of $1 factor                  6.633

Calculate the future value using the table {calculator}          66,330
                            A × R × 1/c =                    A + B + C=
                      (A)          A×i=                              (D)
              Beginning               (B)             (C)       Ending
 Period         Balance          Interest       Payment        Balance

        1               0                0         10,000        10,000

        2          10,000              400         10,000        20,400

        3          20,400              816         10,000        31,216

        4          31,216            1,249         10,000        42,465

        5          42,465            1,699         10,000        54,164

        6          54,164            2,166         10,000        66,330




                               Page 7 of 27
Problem 6.2

                     Future Value of Annuity of $1
                 Given annuity calculate future value
You can deposit $5,000 at the end of each six months into a savings
account that earns an annual interest rate of 14%, compounded semi-
annually. How much will investments grow to at the end of 3 years?
Given:    Annuity [also called PMT]
                                                                $5,000
          Interest rate per year (R)
                                                                  14%
          Years of investment (Y)
                                                                     3
          Payment/compounding periods per year (c)
                                                                     2
          Payment at end of period

Calculate: Interest rate per period (i = R / c)                       7%

            Number of periods (n = Y × c)                              6

            Future value of annuity of $1 factor                  7.153
                                                                 35,765
Calculate the future value using the table {calculator}        {35,766}
                            A × R × 1/c =                    A + B + C=
                      (A)          A×i=                              (D)
              Beginning               (B)              (C)      Ending
 Period         Balance          Interest        Payment       Balance

        1         0               0                5,000      5,000

        2       5,000            350               5,000     10,350

        3      10,350            725               5,000     16,075

        4      16,075           1,125              5,000     22,200

        5      22,200           1,554              5,000     28,754

        6      28,754           2,013              5,000     35,767




                               Page 8 of 27
Problem 7.1

                      Present Value of Annuity of $1
                  Given annuity calculate present value
If Atlantic Corporation could pay $2,500 at the end of each year for six
years, and the interest rate was 7% compounded annually, how much
could Atlantic borrow?
Given:      Annuity [payment]                                     $2,500
            Interest rate per year (R)                               7%
            Length of loan (Y)                                          6
            Payment/compounding periods per year (c)                    1
            Payment at end of period

Calculate: Interest rate per period (i = R / c)                      7%

           Number of periods (n = Y × c)                               6

           Present value of annuity of $1 factor                   4.767
                                                                  11,918
Calculate beginning loan balance (PV) {calculator}              {11,916}
                 A × R × 1/c =                   C–B=            A–D=
           (A)          A×i=                       (D)                (D)
    Beginning              (B)           (C) Reduction           Ending
      Balance         Interest     Payment in balance           Balance

1       11,918               834          2,500      1,666        10,252

2       10,252               718          2,500      1,782         8,470

3         8,470              593          2,500      1,907         6,563

4         6,563              459          2,500      2,041         4,522

5         4,522              317          2,500      2,183         2,339

6         2,339              161          2,500      2,339             0




                               Page 9 of 27
Problem 7.2

                     Present Value of Annuity of $1
                 Given annuity calculate present value
If you could pay $40,000 at the end of each quarter for 1.5 years, and
the annual interest rate on your loan was 16%, compounded quarterly,
how much could you afford to borrow?
Given:     Annuity (payment)
                                                                 $40,000
           Interest rate per year (R)
                                                                    16%
           Length of loan (Y)
                                                                     1.5
           Payment/compounding periods per year (c)
                                                                       4
           Payment at end of period

Calculate: Interest rate per period (i = R / c)                      4%

           Number of periods (n = Y × c)                               6

           Present value of annuity of $1 factor                  5.242
                                                                209,680
Calculate beginning loan balance (PV) {calculator}            {209,685}
                 A × R × 1/c =                   C–B=           A–D=
           (A)          A×i=                       (D)               (D)
    Beginning              (B)           (C) Reduction          Ending
      Balance         Interest     Payment in balance          Balance
1    209,680          8,387          40,000        31,613    178,067
2    178,067          7,123          40,000        32,877    145,190
3    145,190          5,808          40,000        34,192    110,998
4    110,998          4,440          40,000        35,560     75,438
5    75,438           3,018          40,000        36,982     38,456
6    38,456           1,538          40,000        38,462       -6




                               Page 10 of 27
Practice Problems

A. You deposited $6,000 today into a savings account that pays 16%
   interest compounded quarterly. Calculate the amount your
   account will grow to in five years. [13,146] {13,147}

                       Interest rate per period    i = 16% / 4 = 4%
                            Number of periods        n = 5 × 4 = 20
    Present value              FV of $1              Future value
        6,000                   × 2.191                 = 13,146

B. If you deposit $3,000 at the end of each 3 months into an account
   that earns 20% interest compounded quarterly, how much will your
   investments grow to at the end of 4 years? [70,971] {70,972}

                       Interest rate per period    i = 20% / 4 = 5%
                            Number of periods        n = 4 × 4 = 16
       Annuity           FV of annuity of $1         Future value
        3,000                  × 23.657                 = 70,971

C. Assume you want $100,000 at the end of 10 years. If you could
   earn 14% interest compounded semi-annually, how much would
   you need to invest today? [25,800] {25,842}

                       Interest rate per period    i = 14% / 2 = 7%
                            Number of periods       n = 10 × 2 = 20
    Future value               PV of $1              Present value
      100,000                   × 0.258                 = 25,800

D. If you could pay $3,000 at the end of each 6 months for 5 years,
   and the interest rate on your loan was 8% compounded semi-
   annually, how much could you afford to borrow today? [24,333]

                       Interest rate per period     i = 8% / 2 = 4%
                            Number of periods        n = 5 × 2 = 10
       Annuity           PV of annuity of $1         Present value
        3,000                   × 8.111                 = 24,333




                            Page 11 of 27
E. If you could pay $5,000 at the end of each quarter for 4 years, and
   the interest rate on your loan was 16% compounded quarterly, how
   much could you afford to borrow today? [58,260] {58,261}

                           Interest rate per period        i = 16% / 4 = 4%
                                Number of periods            n = 4 × 4 = 16
         Annuity             PV of annuity of $1             Present value
          5,000                     × 11.652                    = 58,260

F.   You can deposit $2,000 at the end of each 6 months into a savings
     account that earns 12% interest compounded semi-annually. How
     much will your investments grow to at the end of 9 years? [61,812] {61,811}

                           Interest rate per period        i = 12% / 2 = 6%
                                Number of periods            n = 9 × 2 = 18
         Annuity             FV of annuity of $1             Future value
          2,000                     × 30.906                    = 61,812

G. Assume you want $1,000,000 at the end of 20 years. If you could
   earn 12% interest compounded annually, how much would you
   need to invest today? [104,000] {103,667}

                           Interest rate per period       i = 12% / 1 = 12%
                                Number of periods           n = 20 × 1 = 20
      Future value                 PV of $1                 Present value
       1,000,000                    × 0.104                    = 104,000

H. Today you deposited $10,000 in a savings account that pays 18%
   interest compounded semi-annually. Calculate the value of your
   account in ten years. [56,040] {56,044}
                       Interest rate per period  i = 18% / 2 = 9%
                            Number of periods     n = 10 × 2 = 20
    Present value              FV of $1            Future value
        10,000                  × 5.604               = 56,040




                                 Page 12 of 27
Bond Problem 1: Discount

                       Bond Discount Amortization Schedule
Given:       Face value of bond issue (FV)                                      $5,000
             Bond coupon rate (CR)                                                 7%
             Life of bond in years (Y)                                               3
             Compounding periods per year (c)                                        2
             Yield-to-maturity (market rate)(MR)                                  10%
Calculate:   Interest rate per period (i = MR / c)                                 5%
             Number of periods (n = Y × c)                                           6
             Semi-annual payment (I = FV × CR × 1/c)                               175
             Present value of $1 factor (PV$1)                                   0.746
             Present value annuity of $1 factor (PVAnn$1)                        5.076
Calculate:   Present value of face value of bond (FV × PV$1)                     3,730
             Present value of annuity (Annuity × PVAnn$1)                          888
             Market value of bond issue (add two lines above)             4,618 {4,619}
             Original issue discount (FV - PV)                                     382
             Price of bond (Market value / Face value) × 100                     92.36
                   A×MR×1/2=                         B−C=      F(up)−D=          A+D=
             (A)           (B)           (C)          (D)           (F)            (G)
    Beginning        Effective      Annuity      Discount      Discount        Ending
         Balance      Interest     Payment      Amortized   Remaining         Balance
0                                                                  382           4,618
1          4,618          231            175           56          326           4,674
2          4,674          234            175           59          267           4,733
3          4,733          237            175           62          205           4,795
4          4,795          240            175           65          140           4,860
5          4,860          243            175           68           72           4,928
6          4,928          246            175           72            0           5,000




                                   Page 13 of 27
A. Record the journal entry to issue to the bonds.
Account names                                      Debit        Credit
Cash                                                 4,618
Discount on bonds payable                              382
   Bonds payable                                                   5,000

B. Record the journal entry for the first annuity payment.
Account names                                        Debit      Credit
Interest expense                                        231
   Cash                                                              175
   Discount on bonds payable                                          56

C. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                      234
   Cash                                                         175
   Discount on bonds payable                                     59

D. Prepare the related sections of the income statement and the
   balance sheet as of the end of the second period.
                          Income Statement
                        For the second period
Other income (expenses): Interest expense                       $234

                            Balance Sheet
                       End of the second period
Bonds payable                                                     $5,000
Discount on bonds payable                                            267
Net bonds payable                                                  4,733

E. Calculate total interest expense over six periods. [1,432]
  Future value      Present value        Annuity          Interest exp.
     5,000              − 4,618        + (175 × 6)           = 1,432

What did you learn?




                             Page 14 of 27
Bond Problem 2: Discount

                       Bond Discount Amortization Schedule
Given:       Face value of bond issue (FV)                                     $10,000
             Bond coupon rate (CR)                                                 5%
             Life of bond in years (Y)                                               3
             Compounding periods per year (c)                                        2
             Yield-to-maturity (market rate)(MR)                                   8%
Calculate:   Interest rate per period (i = MR / c)                                4.0%
             Number of periods (n = Y × c)                                           6
             Semi-annual payment (I = FV × CR × 1/c)                               250
             Present value of $1 factor (PV$1)                                   0.790
             Present value annuity of $1 factor (PVAnn$1)                        5.242
Calculate:   Present value of face value of bond (FV × PV$1)                     7,900
             Present value of annuity (Annuity × PVAnn$1)                         1,311
             Market value of bond issue (add two lines above)             9,211 {9,214}
             Original issue discount (FV - PV)                                     789
             Price of bond (Market value / Face value) × 100                     92.11
                   A×MR×1/2=                         B−C=      F(up)−D=          A+D=
             (A)           (B)           (C)          (D)           (F)            (G)
    Beginning        Effective      Annuity      Discount      Discount        Ending
         Balance      Interest     Payment      Amortized   Remaining         Balance
0                                                                  789           9,211
1          9,211          368            250          118          671           9,329
2          9,329          373            250          123          548           9,452
3          9,452          378            250          128          420           9,580
4          9,580          383            250          133          287           9,713
5          9,713          389            250          139          148           9,852
6          9,852          394            250          144            4           9,996




                                   Page 15 of 27
Bond Problem 3: Discount

                       Bond Discount Amortization Schedule
Given:       Face value of bond issue (FV)                                $15,000
             Bond coupon rate (CR)                                            9%
             Life of bond in years (Y)                                         3
             Compounding periods per year (c)                                  2
             Yield-to-maturity (market rate)(MR)                             12%
Calculate:   Interest rate per period (i = MR / c)                          6.0%
             Number of periods (n = Y × c)                                     6
             Semi-annual payment (I = FV × CR × 1/c)                         675
             Present value of $1 factor (PV$1)                              0.705
             Present value annuity of $1 factor (PVAnn$1)                   4.917
Calculate:   Present value of face value of bond (FV × PV$1)               10,575
             Present value of annuity (Annuity × PVAnn$1)                   3,319
             Market value of bond issue (add two lines above)              13,894
             Original issue discount (FV - PV)                              1,106
             Price of bond (Market value / Face value) × 100                92.63
                   A×MR×1/2=                         B−C=      F(up)−D=     A+D=
             (A)           (B)           (C)          (D)           (F)       (G)
    Beginning        Effective      Annuity      Discount      Discount   Ending
         Balance      Interest     Payment      Amortized   Remaining     Balance
0                                                                 1,106    13,894
1         13,894          834            675          159          947     14,053
2         14,053          843            675          168          779     14,221
3         14,221          853            675          178          601     14,399
4         14,399          864            675          189          412     14,588
5         14,588          875            675          200          212     14,788
6         14,788          887            675          212            0     15,000




                                   Page 16 of 27
Bond Problem 4: Premium

                       Bond Premium Amortization Schedule
Given:       Face value of bond issue (FV)                               $6,000
             Bond coupon rate (CR)                                         12%
             Life of bond in years (Y)                                        3
             Compounding periods per year (c)                                 2
             Yield-to-maturity (market rate)(MR)                            8%
Calculate:   Interest rate per period (i = MR / c)                          4%
             Number of periods (n = Y × c)                                    6
             Semi-annual payment (I=FV×CR×1/c)                              360
             Present value of $1 factor (PV$1)                            0.790
             Present value annuity of $1 factor (PVAnn$1)                 5.242
Calculate:   Present value of face value of bond (FV × PV$1)              4,740
             Present value of annuity (Annuity × PVAnn$1)                 1,887
             Market value of bond issue (add two lines above)      6,627 {6,629}
             Original issue premium (PV - FV)                               627
           Price of bond (Market value / Face value) × 100               110.45
               A×MR×1/2=                          C-B=      F(up)-D=      A-D=
           (A)            (B)        (C)            (D)           (F)       (G)
                                  Semi-
    Beginning       Effective    annual      Premium        Premium      Ending
      Balance        Interest  Payment      Amortized      Remaining    Balance
0                                                                627      6,627
1        6,627             265           360          95         532      6,532
2        6,532             261           360          99         433      6,433
3        6,433             257           360         103         330      6,330
4        6,330             253           360         107         223      6,223
5        6,223             249           360         111         112      6,112
6        6,112             244           360         112           0      6,000




                                   Page 17 of 27
A. Record the journal entry to issue to the bonds.
Account names                                      Debit        Credit
Cash                                                 6,627
   Premium on bonds payable                                          627
   Bonds payable                                                   6,000

B. Record the journal entry for the first annuity payment.
Account names                                        Debit      Credit
Interest expense                                        265
Premium on bonds payable                                   95
   Cash                                                              360

C. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                      261
Premium on bonds payable                                 99
   Cash                                                         360

D. Prepare the related sections of the income statement and the
   balance sheet as of the end of the third period.
                          Income Statement
                         For the third period
Other income (expenses): Interest expense                       $257

                            Balance Sheet
                          End of third period
Bonds payable                                                     $6,000
Premium on bonds payable                                             330
Net bonds payable                                                  6,330

E. Calculate total interest expense over six periods. [1,533]
  Future value      Present value        Annuity          Interest exp.
     6,000              − 6,627        + (360 × 6)           = 1,533

What did you learn?




                             Page 18 of 27
Bond Problem 5: Premium

                      Bond Premium Amortization Schedule
Given:       Face value of bond issue (FV)                               $12,000
             Bond coupon rate (CR)                                          14%
             Life of bond in years (Y)                                         3
             Compounding periods per year (c)                                  2
             Yield-to-maturity (market rate)(MR)                            10%
Calculate:   Interest rate per period (i = MR / c)                         5.0%
             Number of periods (n = Y × c)                                     6
             Semi-annual payment (I=FV×CR×1/c)                               840
             Present value of $1 factor (PV$1)                             0.746
             Present value annuity of $1 factor (PVAnn$1)                  5.076
Calculate:   Present value of face value of bond (FV × PV$1)               8,952
             Present value of annuity (Annuity × PVAnn$1)                  4,264
             Market value of bond issue (add two lines above)    13,216 {13,218}
             Original issue premium (PV - FV)                              1,216
           Price of bond (Market value / Face value) × 100                110.13
               A×MR×1/2=                          C-B=      F(up)-D=       A-D=
           (A)             (B)        (C)           (D)           (F)        (G)
                                   Semi-
    Beginning        Effective    annual      Premium       Premium      Ending
      Balance         Interest  Payment      Amortized     Remaining    Balance
0                                                               1,216    13,216
1        13,216           661         840           179         1,037    13,037
2        13,037           652         840           188          849     12,849
3        12,849           642         840           198          651     12,651
4        12,651           633         840           207          444     12,444
5        12,444           622         840           218          226     12,226
6        12,226           611         840           229            -3    11,997




                                 Page 19 of 27
Bond Problem 6: Premium

                         Bond Premium Amortization Schedule
Given:         Face value of bond issue (FV)                              $18,000
               Bond coupon rate (CR)                                         16%
               Life of bond in years (Y)                                        3
               Compounding periods per year (c)                                 2
               Yield-to-maturity (market rate)(MR)                           12%
Calculate:     Interest rate per period (i = MR / c)                          6%
               Number of periods (n = Y × c)                                       6
               Semi-annual payment (I=FV×CR×1/c)                            1,440
               Present value of $1 factor (PV$1)                            0.705
               Present value annuity of $1 factor (PVAnn$1)                 4.917
Calculate:     Present value of face value of bond (FV × PV$1)             12,690
               Present value of annuity (Annuity × PVAnn$1)                 7,080
               Market value of bond issue (add two lines above)            19,770
               Original issue premium (PV - FV)                             1,770
           Price of bond (Market value / Face value) × 100                 109.83
               A×MR×1/2=                          C-B=      F(up)-D=        A-D=
           (A)             (B)        (C)           (D)           (F)         (G)
                                   Semi-
    Beginning        Effective    annual      Premium       Premium        Ending
      Balance         Interest  Payment      Amortized     Remaining      Balance
0                                                                 1,770   19,770
1     19,770            1,186          1,440           254        1,516   19,516
2     19,516            1,171          1,440           269        1,247   19,247
3     19,247            1,155          1,440           285        962     18,962
4     18,962            1,138          1,440           302        660     18,660
5     18,660            1,120          1,440           320        340     18,340
6     18,340            1,100          1,440           340         0      18,000




                                     Page 20 of 27
Bond Problem: Issue at Par

                     Bond Issued at Par Amortization Schedule
Given:       Face value of bond issue (FV)                                $20,000
             Bond coupon rate (CR)                                         12.0%
             Life of bond in years (Y)                                         3
             Compounding periods per year (c)                                  2
             Yield-to-maturity (market rate)(MR)                           12.0%
Calculate:   Interest rate per period (i = MR / c)                          6.0%
             Number of periods (n = Y × c)                                     6
             Semi-annual payment (I = FV × CR × 1/c)                        1,200
             Present value of $1 factor (PV$1)                              0.705
             Present value annuity of $1 factor (PVAnn$1)                   4.917
Calculate:   Present value of face value of bond (FV × PV$1)               14,100
             Present value of annuity (Annuity × PVAnn$1)                   5,900
             Market value of bond issue (add two lines above)              20,000
             Original issue discount (FV - PV)                                 0
             Price of bond (Market value / Face value) × 100                 100
                   A×MR×1/2=                         B−C=      F(up)−D=     A+D=
             (A)           (B)             (C)         (D)          (F)       (G)
    Beginning        Effective      Annuity       Discount     Discount   Ending
         Balance      Interest     Payment       Amortized   Remaining    Balance
0                                                                    0     20,000
1         20,000        1,200            1,200          0            0     20,000
2         20,000        1,200            1,200          0            0     20,000
3         20,000        1,200            1,200          0            0     20,000
4         20,000        1,200            1,200          0            0     20,000
5         20,000        1,200            1,200          0            0     20,000
6         20,000        1,200            1,200          0            0     20,000




                                   Page 21 of 27
More Bond Questions

Each bond had a face value of $50,000. Calculate the market value of
each bond, and the total cash received from all five bonds.

          Price = (Market value / Face value of bond) × 100

           Market value = (Price/100) × Face value of bond

                                                    Issue price
        Price                Face value           (Cash received)
   100      (1.00)            × 50,000               = 50,000
    92      (0.92)            × 50,000               = 46,000
   106      (1.06)            × 50,000               = 53,000
    94 ½ (0.945)              × 50,000               = 47,250
   101 ¼ (1.0125)             × 50,000               = 50,625
  Total cash received         250,000                 246,875

What did you learn?




                           Page 22 of 27
More Bond Questions
Bonds with a face value of $25,000 had a coupon rate of 9%, a market
rate of 10%, and a life of ten years.

A. Calculate the cash received when the bonds were sold. [23,445]{23,442}
     Future value              PV of $1           Present value
        25,000                 × 0.377               = 9,425
       Annuity           PV of annuity of $1      Present value
  (25,000 × 0.09 × ½)         × 12.462              = 14,020
                          PV of bond issue          = 23,445

B. Prepare the amortization schedule for the first two periods.
   Beginning Effective               Discount       Discount    Ending
     Balance    Interest Payment Amortized Remaining Balance
0                                                      1,555    23,445
1     23,445       1,172     1,125          47         1,508    23,492
2     23,492       1,175     1,125          50         1,458    23,542

C. Record the journal entry to issue to the bonds.
Account names                                      Debit        Credit
Cash                                                23,445
Discount on bonds payable                            1,555
   Bonds payable                                                  25,000

D. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                     1,175
   Cash                                                       1,125
   Discount on bonds payable                                     50

E. Prepare the balance sheet as of the end of the second period.
                           Balance Sheet
Bonds payable                                                 $25,000
Discount on bonds payable                                        1,458
Net bonds payable                                              23,542

What did you learn?




                             Page 23 of 27
More Bond Questions
Bonds with a face value of $18,000 had a coupon rate of 12%, a
market rate of 10%, and life of ten years.

A. Calculate the cash received when the bonds were sold. [20,245]{20,243}
     Future value              PV of $1           Present value
        18,000                 × 0.377               = 6,786
       Annuity           PV of annuity of $1      Present value
  (18,000 × 0.12 × ½)         × 12.462              = 13,459
                          PV of bond issue          = 20,245

B. Prepare the amortization schedule for the first two periods.
   Beginning Effective               Premium        Premium     Ending
     Balance    Interest Payment Amortized Remaining Balance
0                                                      2,245    20,245
1     20,245       1,012     1,080          68         2,177    20,177
2     20,177       1,009     1,080          71         2,106    20,106

C. Record the journal entry to issue to the bonds.
Account names                                      Debit        Credit
Cash                                                20,245
   Premium on bonds payable                                        2,245
   Bonds payable                                                  18,000

D. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                     1,009
Premium on bonds payable                                 71
   Cash                                                       1,080

E. Prepare the balance sheet as of the end of the second period.
                           Balance Sheet
Bonds payable                                                 $18,000
Premium on bonds payable                                         2,106
Net bonds payable                                              20,106
What did you learn?




                             Page 24 of 27
More Bond Questions
Bonds with a face value of $7,000 sold for $5,396. The bonds had a
coupon rate of 8%, a market rate of 12%, and a life of ten years.

A. Prepare the amortization schedule for the first two periods.
   Beginning Effective               Discount       Discount    Ending
     Balance    Interest Payment Amortized Remaining Balance
0                                                      1,604     5,396
1      5,396        324        280          44         1,560     5,440
2      5,440        326        280          46         1,514     5,486




B. Record the journal entry to issue to the bonds.
Account names                                      Debit     Credit
Cash                                                 5,396
Discount on bonds payable                            1,604
   Bonds payable                                                7,000

C. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                      326
   Cash                                                         280
   Discount on bonds payable                                     46

D. Prepare the balance sheet as of the end of the second period.
                           Balance Sheet
Bonds payable                                                  $7,000
Discount on bonds payable                                        1,514
Net bonds payable                                                5,486

What did you learn?




                            Page 25 of 27
More Bond Questions
Bonds with a face value of $9,000 sold for $9,950. The bonds had a
coupon rate of 16%, a market rate of 14%, and life of ten years.

A. Prepare the amortization schedule for the first two periods.
   Beginning Effective               Premium        Premium     Ending
     Balance    Interest Payment Amortized Remaining Balance
0                                                        950     9,950
1      9,950        697        720          23           927     9,927
2      9,927        695        720          25           902     9,902




B. Record the journal entry to issue to the bonds.
Account names                                      Debit     Credit
Cash                                                 9,950
   Premium on bonds payable                                       950
   Bonds payable                                                9,000

C. Record the journal entry for the second annuity payment.
Account names                                      Debit    Credit
Interest expense                                      695
Premium on bonds payable                                 25
   Cash                                                         720

D. Prepare the balance sheet as of the end of the second period.
                           Balance Sheet
Bonds payable                                                  $9,000
Premium on bonds payable                                           902
Net bonds payable                                                9,902

What did you learn?




                            Page 26 of 27
More Bond Questions
Explain why each account increases and decreases.

                      Bonds payable (liability)
                                          Beginning balance
    Face value of bonds paid         Face value of bonds issued
                                             Ending balance



             Discount on bonds payable (contra-liability)
       Beginning balance
 Add. int. exp. over life of bond, Additional int. exp. for the period,
   debited when bond issued          credited when annuity paid
         Ending balance



            Premium on bonds payable (adjunct-liability)
                                        Beginning balance
       Paid to bondholder              Collected in advance,
 excess payments for the period, excess payments over life bond,
   debited when annuity paid       credited when bond issued
                                          Ending balance




                            Page 27 of 27

				
DOCUMENT INFO
Categories:
Tags:
Stats:
views:126
posted:5/17/2012
language:
pages:27