practice problems by tz2Y8ifA

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									Fin 220 - Practice Problems
      Yomna Ahmed

1.    Assume that you purchase a 6-year, 8 percent savings certificate for $1,000. If interest
      is compounded annually, what will be the value of the certificate when it matures?

      a. $630.17          b. $1,469.33       c. $1,677.10       d. $1,586.87        e.$1,766.33

 2.   A savings certificate similar to the one in the previous problem is available with the
      exception that interest is compounded semiannually. What is the difference between
      the future value of the savings certificate compounded semiannually and the one
      compounded annually?

      a.   The semiannual certificate is worth $14.16 more than the annual certificate.
      b.   The semiannual certificate is worth $14.16 less than the annual certificate.
      c.   The semiannual certificate is worth $21.54 more than the annual certificate.
      d.   The semiannual certificate is worth $21.54 less than the annual certificate.
      e.   The semiannual certificate is worth the same as the annual certificate.

 3.   A friend promises to pay you $600 two years from now if you loan him $500 today.
      What annual interest rate is your friend offering?

      a. 7.55%            b. 8.50%           c. 9.54%           d. 10.75%           e. 11.25%

 4.   At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in just
      over 8 years (some calculators round to 9 years). How long, to the nearest year, would it
      take for the purchasing power of $1 to be cut in half if the inflation rate were only 4
      percent?

      a. 12 years         b. 15 years        c. 18 years        d. 20 years         e. 23
      years


5.    You decide to begin saving toward the purchase of a new car in 5 years. If you put
      $1,000 at the end of each of the next 5 years in a savings account paying 6 percent
      compounded annually, how much will you accumulate after 5 years?

      a. $6,691.13        b. $5,637.09       c. $1,338.23       d. $5,975.32        e.$5,731.94

 6.   Refer to Problem 6. What would be the future value if the payments were made at the
      beginning of each year?

      a. $6,691.13        b. $5,637.09       c. $1,338.23       d. $5,975.32        e.$5,731.94

 7.    What would be the future value if $500 payment for 5 years and the account paid 6
      percent compounded semiannually?

      a. $6,691.13        b. $5,637.09       c. $1,338.23       d. $5,975.32        e.$5,731.94



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8.    How much would you be willing to pay today for an investment that would return $800
      each year at the end of each of the next 6 years? Assume a discount rate of 5 percent.

      a. $5,441.53       b. $4,800.00       c. $3,369.89       d. $4,060.55       e.$4,632.37

9.    You have applied for a mortgage of $60,000 to finance the purchase of a new home.
      The bank will require you to make annual payments of $7,047.55 at the end of each of
      the next 20 years. Determine the interest rate in effect on this mortgage.

      a. 8.0%            b. 9.8%            c. 10.0%           d. 5.1%            e. 11.2%

10.   If you would like to accumulate $7,500 over the next 5 years, how much must you
      deposit each six months, given a 6 percent interest rate and semiannual compounding?

      a. $1,330.47       b. $879.23         c. $654.23         d. $569.00         e.$732.67


11.   What is the present value (t = 0) of the following cash flows if the discount rate is 12
      percent?
            0              1               2              3               4
                  12%
            |               |               |              |               |
            0             2,000           2,000          2,000           3,000

      a. $4,782.43       b. $6710.22        c. $4,221.79       d. $4,041.23       e.$3,997.98

12.   What is the effective annual percentage rate (EAR) of 12 percent compounded
      monthly?

      a. 12.00%          b. 12.55%          c. 12.68%          d. 12.75%          e. 13.00%

13.   A 20-year mortgage of $60,000,rate is 10%. This is an amortized loan. How much
      principal will be repaid in the second year?

      a. $1,152.30       b. $1,725.70       c. $5,895.25       d. $7,047.55       e.$1,047.55


14.   The present value (t = 0) of the following cash flow stream is $11,958.20 when
      discounted at 12 percent annually. What is the value of the missing t = 2 cash flow?
                0            1                    2            3               4
                     12%
                |             |                   |             |              |
             PV = 11,958.20 2,000                 ?           4,000           4,000

      a. $4,000.00       b. $4,500.00       c. $5,000.00       d. $5,500.00       e.$6,000.00

15.   Your company is planning to borrow $1,000,000 on a 5-year, 15 percent, annual
      payment, fully amortized term loan. What fraction of the payment made at the end of
      the second year will represent repayment of principal?

      a. 57.18%          b. 42.82%          c. 50.28%          d. 49.72%          e. 60.27%


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16.    Your firm can borrow from its bank for one month. The loan will have to be “rolled
       over” at the end of the month, but you are sure the rollover will be allowed. The
       simple/annual interest rate is 14 percent, but interest will have to be paid at the end of
       each month, so the bank interest rate is 14 percent, monthly compounding. Alternatively,
       your firm can borrow from an insurance company at a simple/annual interest rate that
       would involve quarterly compounding. What APR would be equivalent to the rate
       charged by the bank?

       a. 12.44%          b. 14.16%          c. 13.55%           d. 13.12%          e. 12.88%

17.   The U.S. government offers two treasury bonds, one selling at interest rate of 6.5%,and
       the other at the interest rate of 8.5%.Why would one bond sell for lower interest rate if
       the issuer is the same on both bonds.
18.    Estimate the default and maturity premiums, given that Treasury bills interest rate is
       2%,20 years Treasury bond =6% and 20 years AAA corporate bond is 9%.


19.


       Nominal Rate        Inflation Rate          Real    rate    using Real Rate using the
                                                   Approx. equation      true equation
       13%                 5%




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Answers:
1.   d.     0           1                2           3            4               5       6
             | 8%       |                |           |            |               |       |
          -1,000                                                                      FV6 = ?

          input N = 6, I = 8, PV = -1000,and solve for FV = $1,586.87.


2.   a.     0               1                2              3                4                  5        6 Years
            0     1         2        3       4       5      6         7      8        9       10    11 12 Periods
               4%
             |    |         |        |       |       |      |         |      |        |        |     |   |
          -1,000                                                                                    FV12 = ?

          input N = 12, I = 4, PV = -1000 and then solve for FV = $1,601.03. The
          difference, $1,601.03 – $1,586.87 = $14.16.


3.   c. 0 1       k=?            2
          |                      |                    |
        -500                                         600

          input N = 2, PV = -500, FV = 600, and solve for I = 9.54%.


4.   c. 0N = ?
              4%
        | |
        1.00                    0.50

          input I = 4, PV = -1.00, and FV = 0.50. Solve for N = 17.67 ≈ 18 years.




5.   b. 0              1                  2               3                4              5
        || 6%           |                  |               |                |
                      1,000              1,000           1,000            1,000      1,000
                                                                                  FVA5 = ?
          input N = 5, I = 6, PMT = 1000, and solve for FV = $5,637.09.



6.   d. 0 1               2                    3                  4                 5
        | | 6%            |                     |                  |                |
        1,000           1,000                1,000              1,000             1,000 FVA5 = ?
          switch to “BEG” mode, then input N = 5, I = 6, PMT = 1,000, and solve for FV =
          $5,975.32.


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 7.   e. 0 3%         1                      2                 3                       4              5
             Years
         0     1      2            3         4         5       6             7         8      9     10
            Periods
         ||    |      |         |             |      |          |       |            |        |
         500 500    500       500           500    500        500     500          500      500
                                                                                              FVA10 = ?
           input N = 10, I = 3, PMT = 500, and solve for FV = $5,731.94.



8.    d.       0     1           2             3          4          5             6
                  5%
               |     |           |             |          |          |             |
           PVA = ? 800         800           800        800        800           800

           input   N    =     6,        I     =    5,      PMT           =       800,      and    solve   for
           PV = $4,060.55.


9.    c.     0        1                  2          3                               20
                k=?
             |        |                  |           |              •••              |
           60,000   7,047.55           7,047.55    7,047.55                        7,047.55

           input N = 20, PV = -60000, PMT = 7047.55, and solve for I = 10.00%.


10.   c. 0              1       2       3       4        5
               Years
           0 3% 1       2   3   4   5   6   7   8   9   10
              Periods
           ||    |      |   |   |   |   |   |   |   |
           PMT        PMT PMT PMT PMT PMT PMT PMT PMT PMT
                                                       7,500

           input N = 10, I = 3, FV = 7500, and solve for PMT = $654.23.




11.   b. Discount each cash flows to year zero, then add all the PVs ,i.e. 2000/1.12
         +2000/(1.12^2)+2000/(1.12^3)+3000/(1.12^4), = $6710.22


12.   c. EAR = (1 + APR/m)m – 1.0
             = (1 + 0.12/12)12 – 1.0


                                                   5
                   = (1.01)12 – 1.0
                   = 1.1268 – 1.0
                   = 0.1268 = 12.68%.


13.      a.
Period            Beginning           Payment                Interest           Principal         Ending Balance
                  Balance                                                       Reduction
1                 60,0000             7,047.55               6,000              1,047.55          58,952.45
2                 58,952.45           7,047.55               5,895.25           1,152.30          57,800.15

14.      e. Add 2000/(1.12)+ 4000/(1.12^3)+4000/(1.12^4) =7,174.9.Then deduct what you
             get from the total present value so 11,958.20-7,174.9=4,783.3.The missing cash
             flow has a present value of 4,783.3.
            4783.3= missing cash flow /(1.12^2)
               Therefore, the missing cash flow is equal to 6,000.


15.      a. N = 5, I = 15, PV = 1000000, to solve for PMT = $298,315.55.


              Period        Beginning       Payment                Interest        Principal       Ending
                            Balance                                expense         Reduction       Balance
              1             1,000,000       298,315.55             150,000         148,315.55      851,684.45
              2             851,684.45      298,315.55             127,752.67      170,562.88      681,121.57
The fraction that is principal is $170,562.88/$298,315.55 = 57.18%.


16.      b. Start with a time line to picture the situation:

              Bank: APR = 14%; EAR = ?

              0    1    2         3    4     5       6         7        8   9     10    11   12
              |    |    |         |    |     |       |         |        |   |      |     |    |

              Insurance company: EAR = 14.93%; APR=?

              0               1                  2                      3              4
              |               |                  |                      |              |


Note that simple rate is the another name for APR.

              EAR = (1 +APR /12)12 – 1
                  = (1 + 0.14/12)12 – 1
                  = 14.93%.

              14.93% = (1 + APR/4)4 – 1
               1.1493 = (1 + APR /4)4
               1.0354 = 1 + APR /4
               0.0354 = APR /4
               APR = 14.16%.


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17. The difference could be because of maturity risk premium.

18. Maturity Risk premium =6%-2%=4%.
    Default Risk premium= 9%-6%=3%

19. Approximate Real Rate 13% 5% 8%
   True Real Rate 1.13/1.05) 1 1.0762 1 0.0762 or 7.62%




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