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.





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.

a.
Using a financial calculator, enter: PV = (-)1,000, FV = 0, I = 8%, n = 4, and compute PMT = $301.92

b.
Time Loan balance Year-end interest due Year-end payment Amortization of loan
0 $1,000.00 $80.00 $301.92 $221.92
1 $778.08 $62.25 $301.92 $239.67
2 $538.41 $43.07 $301.92 $258.85
3 $279.56 $22.36 $301.92 $279.56
4 $ 0.00 $ 0.00 -- --
c. PV=
Therefore, the loan balance is $778.08 after one year.