EXERCISES
1. Go to the Federal Reserve Web site, https://www.federalreserve.gov. Go to "Economic Research and Data," and access "Recent Statistical Releases" and then "Consumer Credit." Find average interest rates charged by commercial banks on new automobile loans, personal loans, and credit card plans.
a. Compare the average level of interest rates among the three types of loans.
8/2015
48-month new car loan 4.11%
24-month personal loan 9.98%
Credit card plans (interest) 12.22%
b. Access "Historical Data" and then "Consumer Credit," and compare trends in the cost of consumer credit provided by commercial banks over the past three years.
2012 2013 2014
48-month new car loan 4.91% 4.43% 4.24%
24-month personal loan 10.71% 10.20% 10.22%
Credit card plans (interest) 12.06% 11.91% 11.87%
2. Find the future value of $10,000 invested now after five years if the annual interest rate is 8 percent.
a. What would be the future value if the interest rate is a simple interest rate?
$10,000(0.08) = $800 interest per year
$800 x 5 = $4,000 total interest
FV = $10,000 + $4,000 = $14,000
b. What would be the future value if the interest rate is a compound interest rate?
FV5 = PV(1 + r)5
FV5 = $10,000(1 + 0.08)5
FV5 = $10,000(1.08)5
FV5 = $10,000(1.469)
FV5 = $14,690
3. Determine the future values if $5,000 is invested in each of the following situations:
a. 5 percent for ten years
FV10 = $5,000(1+0.05)10
FV10 = $5,000(1.05)10
FV10 = $5,000(1.629)
FV10 = $8,145
b. 7 percent for seven years
FV7 = $5,000(1+0.07)7
FV7 = $5,000(1.07)7
FV7 = $5,000(1.606)
FV7 = $8,030
c. 9 percent for four years
FV4 = $5,000(1+0.09)4
FV4 = $5,000(1.09)4
FV4 = $5,000(1.412)
FV4 = $7,060
4. You are planning to invest $2,500 today for three years at a nominal interest rate of 9 percent with annual compounding.
a. What would be the future value of your investment?
FV3 = $2,500(1 + 0.09)3
FV3 = $2,500(1.09)3
FV3 = $2,500(1.295)
FV3 = $3,237.50
b. Now assume that inflation is expected to be 3 percent per year over the same three-year period. What would be the investment's future value in terms of purchasing power?
9% (interest) - 3% (inflation) = 6% purchasing power rate
FV3 = $2,500(1 + 0.06)3
FV3 = $2,500(1.06)3
FV3 = $2,500(1.191)
FV3 = $2,977.50
c. What would be the investment's future value in terms of purchasing power if inflation occurs at a 9 percent annual rate?
9% (interest) - 9% (inflation) = 0% purchasing power rate
FV3 = $2,500(1 + 0.00)3
FV3 = $2,500(1.000)
FV3 = $2,500
5. Find the present value of $7,000 to be received one year from now assuming a 3 percent annual discount interest rate. Also calculate the present value if the $7,000 is received after two years.
PV = FVn / (1 + r)n
PV(received one year from now) = $7,000 / (1 + 0.03)1
PV = $7,000 / (1.03)
PV = $6,796.12
PV(received 2 years from now) = $7,000 / [(1 + 0.03)(1 + 0.03)]
PV = $7,000 / 1.0609
PV = $6,598.17
6. Determine the present values if $5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations:
a. 5 percent for ten years
PV = FVn / (1 + r)n
PV = $5,000 / (1+0.05)10
PV = $5,000 / (1.05)10
PV = $5,000 / (0.614)
PV = $3,070
b. 7 percent for seven years
PV = FVn / (1 + r)n
PV = $5,000 / (1 + 0.07)7
PV = $5,000 / (0.623)
PV = $3,115
c. 9 percent for four years
PV = FVn / (1 + r)n
PV = $5,000 / (1 + 0.09)4
PV = $5,000 / (1.09)4
PV = $5,000 / 0.708
PV = $3,540
7. Determine the present value if $15,000 is to be received at the end of eight years and the discount rate is 9 percent.
PV = FVn / (1 + r)n
PV = $15,000 / (1 + 0.09)8
PV = $15,000 / (1.09)8
PV = $15,000 / (0.502)
PV = $7,530
How would your answer change if you had to wait six years to receive the $15,000?
PV = FVn / (1 + r)n
PV = $15,000 / (1 + 0.09)6
PV = $15,000 / (1.09)6
PV = $15,000 / 0.596
PV = $8,940
8. Determine the future value at the end of two years of an investment of $3,000 made now and an additional $3,000 made one year from now if the compound annual interest rate is 4 percent.
FVn = PV(1 + r)n + PV(1 +r)
FV2 = $3,000(1 + 0.04)2 + $3,000(1 + 0.04)
FV2 = $3,000(1.0816) + $3,000(1.04)
FV2 = $3,244.8 + $3,120 = $6,364.80
16. Use a financial calculator or computer software program to answer the following questions:
a. What would be the future value of $15,555 invested now if it earns interest at 14.5 percent for seven years?
Using a financial calculator, enter 15555 and press PV, enter 14.5 and press %i, and enter 7 and press N. Then, press CPT and FV which gives an answer of 40133.63 or $40,133.63.
Using Excel, click financial wizard, then FV, enter 0.14 for rate, 7 for n per, 0 for pmt, 15,555 for PV, 0 for type.
b. What would be the future value of $19,378 invested now if the money remains deposited for eight years and the annual interest rate is 18 percent?
Using a financial calculator, enter 19378 and press PV, enter 18 and press %i, and enter 8 and press N. Then, press CPT and FV which gives an answer of 72839.17 or $72,839.17.
Using Excel, click financial wizard, then FV, enter 0.18 for rate, 8 for nper, 0 for pmt, 19,378 for PV, 0 for type.
17. Use a financial calculator or computer software program to answer the following questions:
a. What is the present value of $359,000 that is to be received at the end of 23 years if the discount rate is 11 percent?
Using Excel, click financial wizard, then FV, enter 0.11 for rate, 23 for nper, 0 for pmt, 359,000 for PV, 0 for type.
b. How would your answer change in Part (a) if the $359,000 is to be received at the end of 20 years?
Using Excel, click financial wizard, then FV, enter 0.11 for rate, 20 for nper, 0 for pmt, 359,000 for PV, 0 for type.
19. Use a financial calculator or computer software program to answer the following questions.
a. What would be the future value of $19,378 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and interest on the investment is compounded semiannually?
Using a financial calculator, enter 19378 and press PV, enter 9.00 (18/2) and press %i, and enter 16 (8 × 2) and press N. Then, press CPT and FV which gives an answer of 76936.59 or $76,936.59.
Using Excel, click financial wizard, then FV, enter 0.09 for rate (18/2), 16 for nper (8x2), 0 for pmt, 19,378 for PV, 0 for type.
c. How would your answer for (a) change if quarterly compounding were used?
Using a financial calculator, enter 19378 and press PV, enter 4.50 (18/4) and press %i, and enter 32 (8 × 4) and press N. Then, press CPT and FV which gives an answer of 79255.65 or $79,255.65.
Using Excel, click financial wizard, then FV, enter 0.045 for rate (18/4), 32 for nper (8x4), 0 for pmt, 19,378 for PV, and 0 for type.