# Amortizing Loan

38. Amortizing Loan. 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.

Time Loan Balance Year-end Interest Year-end Payment Amortization of Loan

Due on Balance

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.

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