Question

Jan sold her house on December 31 and took a $30,000 mortgage as part of the payment. The 10-year mortgage has an 11% 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? Round your answer to the nearest cent.

b. How much interest was included in the first payment? Round your answer to the nearest cent.
How much repayment of principal was included? Do not round intermediate calculations. Round your answer to the nearest cent.

c. How much interest must Jan report on Schedule B for the first year? Do not round intermediate calculations. Round your answer to the nearest cent.
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

a. Mortgage = Loan = $30000, Nominal interest rate = 11%, No of years in mortgage = 10 years

As payment for mortgage are made semi annually, therefore

Semi annual rate = Nominal rate / 2 = 11% / 2 = 5.50%

No of payments or half years in mortgage = 2 x no of years in mortgage = 2 x 10 = 20

We can find the dollar amount of each payment using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get dollar amount of each payment = 2510.3799 = $2510.38 (rounded to nearest cent)

Hence dollar amount of each payment Jan receives = $2510.38

b. Interest for a half year = Beginning balance of a half year x semi annual interest rate

Beginning balance of first half year ending June 30 = Mortgage = $30000

Hence interest included in first payment = Interest for first half year = Beginning balance for first half year x semi annual interest rate = 30000 x 5.5% = 1650

Hence Interest included in first payment = $1650.00

Principal included in first payment = dollar amount of each payment - interest included in first payment = 2510.38 - 1650 = 860.38

Principal included in first payment = $860.38

c. Ending balance for first half year = Beginning balance of first half year - Principal included in first payment = 30000 - 860.38 = 29139.62

Ending balance for first half year = Beginning balance for second half year = 29139.62

Interest included in second payment = Interest for second half year = Beginning balance for second half year x semi annual rate = 29139.62 x 5.5% = 1602.6791

Amount of interest to be reported in Schedule B in first year = Interest included in first payment + Interest included in second payment = 1650 + 1602.6791 = 3252.6791 = $3252.68 (rounded to nearest cent)

Amount of interest to included in Schedule B in first year = $3252.68

No, interest income will not remain same next year. Dollar amount of each payment Jan receives consist of both principal and interest. As payments are made, principal is being repaid along with interest. Due to this beginning balance of loan for each subsequent half year will decrease. Hence the interest for each subsequent half year will also decrease. So interest income will change ever year.

d) It is known that each payment contains both principal and interest component. Outstanding balance of loan for each half year is reduced as payments are received. This is so because principal is repaid when payments are made for loan. As outstanding balance is reduced ever subsequent half year, so interest for a half year is also reduced every subsequent half year. This results in change in interest income every year.