Question

jan sold her house on December 31 and took a $40,000 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? 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? The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases. The portion of the payment that is applied to interest increases, while the portion of the payment that is applied to principal decreases. 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. The portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal also declines. 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? d. If the payments are constant, why does the amount of interest income change over time? As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal increases. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal declines. As the loan is amortized (paid off), the beginning balance, hence the interest charge, increases and the repayment of principal declines. 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

a.) $3209.7

b.)

First payment: $2000 (interest): $1209.7 (principal repayment)

Second payment: $$1939.52 (interest) : $1270.2 (principal repayment)

c.) $3939.52: No, interest income for the next year will change.

d.) The basis for computing interest is the value of the mortgage which is declining as payments are made.

EXPLANATIONS:-

a.)

Given:

Present value (PV) = $40000

Interest rate (r) = 10%

Time in years (t) = 10 years

Compounding periods (n) = semiannually ( 2 times per year)

Required : Annuity payments (PMT)

Where,

PV = present value of ordinary annuity

PMT = annuity payments

r =nominal interest rate

n = number of compounding period per year

t = number of years

b.)

First payment:

interest included in the first payment is equal to the present value of the mortgage (now still at $40,000) multiplied by periodic interest rate of 5% (10% / 2)

=$40,000 * .05

=$2,000

the payment that goes to principal is equal to the monthly payment less interest:

=$3209.7 - $2000

= $1209.7

Second payment:

After first payment, the remaining value of the mortgage is:

=$40,000 - $1209.7

= $38,790

That amount will be used as the basis for next period interest.

Interest:

=$38,790 * 0.05

=$1939.5

Reduction of principal:

=$3209.7 - $1939.5

= $1270.2

c.)

The interest that must be reported on Schedule b for the first year is the sum of the interest earned on the first twi payments:

= $2000 + $1939.5

= $3939.5

Interest income for the next year will not be the same, it will gradually decrease over the life of the mortgage.

d.)

The amount of interest income change over time since the basis for computing interest is the value of mortgage which is declining as payments are made, Just as illustrated in parts b and c.