Question

Assume that your aunt sold her house on december 31, and that she took a mortgage in the amount of $10,000 as part of the payment. the mortgage has a quoted (or nominal) interest rate of 10 percent, but it calls for payments every 6 months, beginning on june 30, and the mortgage is to be amortized over 10 years. now, one year later, your aunt must file schedule b of her tax return with the irs, informing them of the interest that was included in the 2 payments made during the year. (this interest will be income to your aunt and a deduction to the buyer of the house.) to the closest dollar, what is the total amount of interest that was paid during the first year?

Answer 1

To answer the student's question, one would first calculate the semi-annual payment for the mortgage, then allocate the portion of each payment that is interest for the first year.

Step-by-step explanation:

The student's question involves calculating the total amount of interest paid during the first year on a $10,000 mortgage with a nominal interest rate of 10%, with semi-annual payments over a period of 10 years.

First, we determine the semi-annual interest rate by dividing the annual nominal interest rate by two, which is 10% / 2 = 5% per half year. Next, we calculate the mortgage payment using the formula for an amortizing loan payment. Finally, since payments start six months after the loan is taken out, there would be exactly two payments made in the first year.

To calculate the interest paid in each payment, we subtract the principal paid (total payment minus interest) from the total payment. Initially, the entire loan amount is subject to interest, so the first interest payment would be larger than the second, as part of the loan principal would have been paid down by the first payment.