44.8k views
0 votes
A mortgage for $104,000 is made with initial payments of $500 per month for the first year. The interest rate is 9 percent. After the first year, payments will increase to an amount that makes the loan fully amortized over the remaining 24 years with constant monthly payments.

a. Calculate the interest deductions for the loan for the first year.
b. How much, if any, interest must be deferred until the second year?
c. How much interest will be deducted in the second year?

User Edd Turtle
by
7.7k points

1 Answer

5 votes

Final answer:

To compute interest deductions and understand loan amortization, it is necessary to calculate interest on a monthly basis, considering payment changes and outstanding balances over the loan's term. Deferred interest and future deductions depend on the loan terms and payment structure.

Step-by-step explanation:

The subject of the student's question involves calculating interest deductions and loan amortization for a mortgage, which falls into the realm of financial mathematics. The grade level is suitable for college students, particularly those studying finance or related fields.

Interest Deductions for the First Year

To calculate the interest deductions for the first year, we need to determine how much interest is accrued each month on the outstanding balance of the mortgage and sum it across all payments made in the year. The initial balance is $104,000 with a 9% annual interest rate, which gives a monthly interest rate of 0.09/12. Multiplying the monthly interest rate by the unpaid balance gives us the interest for that month. Then, subtract $500, the monthly payment, from the interest amount to find out how much the principal is reduced and use the new balance to repeat the calculation for the following month.

Deferring Interest to the Second Year

If the monthly payment is less than the interest charged for that month, the unpaid interest must be deferred until the next month and added to the loan balance, potentially leading to what is commonly referred to as negative amortization.

Interest Deductible in the Second Year

The interest deductible in the second year can be calculated in a similar manner as the first year, using the new balance and payment amount. However, now the payments will need to be recalculated to ensure that they are sufficient to fully amortize the remaining balance over the next 24 years.

User Jonatjano
by
8.1k points