# Various finance problems: AT&T bond, General Motors bond and calculating a loan balance

37. Consider a 4-year amortizing loan. You borrow $1,000 initially, and repay it in four equal annual year-end payments a. If the interest rate is 8 percent, show that the annual payment is $301.92.

b. Fill in the following table, which shows how much of each payment is interest versus principal repayment (that is, amortization), and the outstanding balance on the loan at each date.

Loan Year-End Interest Year-End Amortization

Time Balance Due on Balance Payment of Loan

0 $1,000 $80 $301.92 $221.92

1 ________ __________ 301.92 _______

2 ________ __________ 301.92 _______

3 ________ __________ 301.92 _______

4 0 0 ___ ___

c. Show that the loan balance after 1 year is equal to the year-end payment of $301.92 times the 3-year annuity factor.

11. A General Motors bond carries a coupon rate of 8 percent, has 9 years until maturity, and sells at a yield to maturity of 7 percent.

a. What interest payments do bondholders receive each year?

b. At what price does the bond sell? (Assume annual interest payments.)

c. What will happen to the bond price if the yield to maturity falls to 6 percent?

6. An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for $1,100.

a. What is the current yield on the bond?

b. What is the yield to maturity?

PS what is (1.06) raised to the 40th power?

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