Question

Jan sold her house on December 31 and took a $15,000 mortgage as part of the payment. The 10-year mortgage has a 12% 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.

$ _________  

How do these values change for the second payment?

1. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases.
2. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal decreases.
3. The portion of the payment that is applied to interest and the portion of the payment that is applied to principal remains the same throughout the life of the loan.
4. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal also declines.
5. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal also increases.

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?
a) Her interest income will increase in each successive year.

b) Her interest income will remain the same in each successive year.

c) She will not receive interest income, only a return of capital.

d) Her interest income will decline in each successive year.

e) She will receive interest only when the mortgage is paid off in 10 years.

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

1. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal increases.
2. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases.
3. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal declines.
4. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal declines.
5. As the loan is amortized (paid off), the beginning balance declines, but the interest charge and the repayment of principal remain the same.

Answer 1

Formula for Equal monthly payment can be used to compute semiannual payment as:

EMI = P × r × (1 + r) ⁿ / {(1 + r) ⁿ - 1}

Where,

P = Principal = $ 15,000

r = rate of interest = 12 % p.a. or 0.12/2 = 0.06 semiannually

n = No. of periods = 10 x 2 = 20 periods

Equal semiannual payment = $ 15,000 x 0.06 x (1 + 0.06)²⁰ / {(1 + 0.06) ²⁰ -1}

                                         = $ 15,000 x 0.06 x (1.06)²⁰ / {(1.06) ²⁰ -1}

                                         = $ 15,000 x 0.06 x 3.20713547221285/ (3.20713547221285 -1)

                                         = $ 15,000 x 0.06 x 3.20713547221285/2.20713547221285

                                         = $ 15,000 x 0.06 x 1.45307594961419

                                         = $ 1,307.76835465277 or $ 1,307.77

a.

Amount of each semiannual payment is $ 1,307.77

b.

Interest in first payment = Principal x periodic rate = $ 15,000 x 0.06 = $ 900

Interest of $ 900 is included in first payment.

Repayment of principal = Semiannual payment – Interest payment

                                  = $ 1,307.77 - $ 900 = $ 407.77

Repayment of principal included in first payment is $ 407.77

On progress of loan tenure, principal goes on decreasing, as a part of payment is considered as interest and rest are used to deduct the principal. So payment for interest portion goes on decreasing along with diminished principal. This leads to increase in payment portion for principal repayment as each payments are consistent.

Hence option “I. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases” is correct answer.

c.

Interest portion for 2^nd payment = Balance principal x periodic rate

                                            = ($ 15,000 - $ 407.77) x 0.06

                                              = $ 14,592.23 x 0.06 = $ 875.53

Total interest for first year = $ 900 + $ 875.53 = $ 1,775.53

Jan report should report $ 1,775.53 of interest for first year on Schedule B.

No, the interest income will not be same for next year.

As balance principal goes on decreasing for successive payments, interest payment for the principal also goes on decreasing as interest rate is constant throughout the loan period.

Hence Option “d) Her interest income will decline in each successive year” is correct answer.

d.

During the loan period, balance principal and its interest charge both decreases simultaneously which causes principal repayment portion to increase.

Hence Option “II. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases” is correct answer.