Question

Jan sold her house on December 31 and took a $25,000 mortgage as part of the payment. The 10-year mortgage has a 7% 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? -Select- I. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases II. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal decreases II. 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 IV. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal also declines. V. 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? Select- d. If the payments are constant, why does the amount of interest income change over time? -Select- I. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal increases. II. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases II. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal declines V. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal declines V. 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 EMI can be used to compute semiannual payment as:

Equal Semiannual payment = P × r × (1 + r) ⁿ /{(1 + r)ⁿ - 1 }

Where,

P = Principal= $ 25,000

r = rate of interest = 7 % p.a. or 0.07/2 = 0.035 semiannually

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

Equal semiannual payment = $ 25,000 x 0.035 x (1 + 0.035)²⁰ / {(1 + 0.035) ²⁰ -1}

                                            = $ 25,000 x 0.035 x (1.035)²⁰ / {(1.035) ²⁰ -1}

                                            = $ 25,000 x 0.035 x 1.989788863/ {(1.989788863-1}

                                            = $ 25,000 x 0.035 x 1.989788863/ (0.989788863)

                                            = $ 25,000 x 0.035 x 2.01031648

                                            = $ 1,759.02692 or $ 1,759.03

a.

Dollar amount of each payment is $ 1,759.03

b.

Interest in first payment = Periodic rate x Beginning principal = 0.035 x $ 25,000 = $ 875.00

Principal repayment in first payment = Semiannual payment – Interest amount

                                                                  = $ 1,759.03 - $ 875.00 = $ 884.03

Balance principal after first payment = Begining principal - Principal repayment

                                                                  = $ 25,000 - $ 884.03 = $ 24,115.97

Interest in second payment = Periodic rate x Balance principal = 0.035 x $ 24,115.97 = $ 844.06

Principal repayment in second payment = Semiannual payment – Interest amount

                                                                  = $ 1,759.03 - $ 844.06 = $ 914.97

On progression of loan payments, principal goes on decreasing and hence interest amount also decreases. Each payment being equal, principal repayment goes on increasing.

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

c.

Total interest for first year = $ 875.00 + $ 844.06 = $ 1,719.06

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

d.

Each and every payment of loan is equal but interest and principal repayment portions are different. Principal amount goes on reducing on progression of loan period. So interest for this diminished principal also decreases gradually. Hence principal repayment portion increases for each successive payment.

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