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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

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