Question

5-22 LOAN AMORTIZATION Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year.

a. What is the dollar amount of each payment Jan receives?

b. How much interest was included in the first payment? How much repayment of principal was included? How do these values change for the second payment?

c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year?

d. If the payments are constant, why does the amount of interest income change over time?

Answer 1

Semi-annual rate = 10%/2 = 5%

Number of periods = 10*2 = 20

Amount of payment = Amount of Loan/Present value annuity factor

= 10,000/PVAF(5%, 20 periods)

= 10,000/12.4622103416

i.e. $802.43

Interest in first payment = 10,000*5% = $500

Principal repaid = 802.43 – 500 = $302.43

In Second half yearly payment = (10,000-302.43)*5% = $484.88

I.Portion of interest declines and portion of principal increases

Hence, interest paid during first year = 500+484.88 = $984.88

d.IIThe beginning balance, interest charge declines and repayment of principal increases

Interest income will decline in each successive year