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 10 percent, show that the annual payment is $315.47.

b. Fill in the following table, which shows how much of each payment is comprised of 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 $100 $315.47 $215.47

1 ——— ——— 315.47 ———

2 ——— ——— 315.47 ———

3 ——— ——— 315.47 ———

4 0 0 — —

c. Show that the loan balance after 1 year is equal to the year-end payment of $315.47 times the 3-year annuity factor.