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# Effective Annual Rates and Calculating Monthly Payments

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Merchants Bank offers to lend you \$30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the \$30,000, but it will charge 7.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

a. 1.49%

b. 1.24%

c. 1.04%

d. 0.86%

e. 0.69%

You are considering investing in a bank account that pays a nominal annual rate of 6%, compounded monthly. If you invest \$5,000 at the end of each month, how many months will it take for your account to grow to \$200,000? Round fractional years up.

a. 33

b. 37

c. 41

d. 45

e. 49

Suppose you take out a \$10,000 loan at a 6% nominal annual rate. The terms of the loan require you to make 12 equal end-of-month payments each year for 4 years, and then an additional final (balloon) payment of \$4,000 at the end of the last month. What will your equal monthly payments be?

a. \$131.06

b. \$137.96

c. \$145.22

d. \$152.86

e. \$160.91

What's the present value of \$1,500 discounted back 5 years if the appropriate interest rate is 6%, compounded semiannually?

a. \$956.95

b. \$1,007.32

c. \$1,060.33

d. \$1,116.14

e. \$1,171.95

P. Lange Inc. hired your consulting firm to help them estimate the cost of equity. The yield on Lange's bonds is 7.25%, and your firm's economists believe that the cost of equity can be estimated using a risk premium of 3.50% over a firm's own cost of debt. What is an estimate of Lange's cost of equity from retained earnings?

a. 10.75%

b. 11.18%

c. 11.63%

d. 12.09%

e. 12.58%

Stock A has a beta = 0.8, while Stock B has a beta = 1.6. Which of the following statements is CORRECT?

a. Stock B's required return is double that of Stock A's.

b. If the marginal investor becomes more risk averse, the required return on Stock B will increase by more than the required return on Stock A.

c. An equally weighted portfolio of Stocks A and B will have a beta lower than 1.2.

d. If the marginal investor becomes more risk averse, the required return on Stock A will increase by more than the required return on Stock B.

e. If the risk-free rate increases but the market risk premium remains constant, the required return on Stock A will increase by more than that on Stock B.

#### Solution Preview

Merchants Bank offers to lend you \$30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the \$30,000, but it will charge 7.0%, simple interest, with interest
paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

Effective annual rate for merchant bank = (1+6%/4)^4-1=0.0614 or 6.14%
Effective annual rate for Gold cost bank = 7%
Difference in the effective annual rates charged by the two banks= 7%-6.14%=0.86%