# Homework 3

E1- Go to the Federal Reserve Web site, http://www.federalreserve.gov. Go to “Economic Research and Data” and access “Consumer Credit”. Find interest rates charged by commercial banks on new automobile loans, personal loans, and credit card plans.

Reported as of 1/8/2018:

Auto Loans- 4.81 (48 months), 4.51 (60 months)

Personal Loans- 10.57

Credit cards- All accounts (13.16) Accounts assessed interest (14.99)

Compare trends in the cost of consumer credit provided by commercial banks over the past three years.

Credit card interest rates are extremely high compared to the other loans.

P2- 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 * [1+ (8%) * (5)]

10,000 * 1.4

FV=\$14,000

b. What would be the future value if the interest rate is a compound interest rate?

10,000 * (1.08) ^5

10,000 * 1.469

FV=\$14,690.00

P3- Determine the future values (FVs) if \$5,000 is invested in each of the following situations:

a.5 percent for ten years

\$8,144.47

b.7 percent for seven years

\$8,028.91

c.9 percent for four years

\$7,057.91

P4- 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 (FV) of your investment?

\$2500 * (1.09) ^ 3

FV= \$3,237,57

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 FV in terms of purchasing power?

(9%-3%) = 6%

2500 (1.06) ^ 3

=\$2,977.54

c. What would be the investment’s FV in terms of purchasing power if inflation occurs at a 9 percent annual rate?

In this case if inflation is 9% annual rate, it is the same was the interest rate. Therefore, the purchasing power is the same. Purchasing power of \$2500 will be the same over time.

P5- Find the present value (PV) of \$7,000 to be received one year from now assuming a 3 percent annual discount interest rate.

\$7000/1.03= \$6,796.12

Also calculate the PV if the \$7,000 is received after two years.

\$7,000/1.03 ^2 = \$6,598.17

P7- Determine the present value if \$15,000 is to be received at the end of eight years and the discount rate is 9 percent. How would your answer change if you had to wait six years to receive the \$15,000?

Present Value= 15,000* PV Factor

=15000*.502

=\$7530.00

Present Value for 6 yrs= 15000*PV Factor

=15000*.596

=\$8940.00

P16- Use a financial calculator or computer software program to answer the following questions:

a. What would be the future value (FV) of \$15,555 invested now if it earns interest at 14.5 percent for seven years?

\$15,555*(1.145)^7

=\$40,133.62

b. What would be the FV of \$19,378 invested now if the money remains deposited for eight years and the annual interest rate is 18 percent?

\$19,738*(1.18)^8

=\$72,839.17

P17- Use a financial calculator or computer software program to answer the following questions:

a. What is the present value (PV) of \$359,000 that is to be received at the end of 23 years if the discount rate is 11 percent?

=\$32,558.62

b. How would your answer change in (a) if the \$359,000 is to be received at the end of 20 years?

=44,528.17

P19- Use a financial calculator or computer software program to answer the following questions.

a. What would be the future value (FV) 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?

\$19,738*(1.09)^16

FV=\$76,936.59

b. How would your answer for (a) change if quarterly compounding were used?

\$19,738*(1.045)^32

FV=\$79,255.65

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