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An interest only ARM is made for $212,000 for 30 years. The start rate is 5 percent and the borrower will (1) make monthly interest only payments for 3 years. Payments thereafter must be sufficient to fully amortize the loan at maturity.

a. If the borrower makes interest only payments for 3 years, what will payments be?
b. Assume that at the end of year 3, the reset rate is 6 percent. The borrower must now make payments so as to fully amortize the loan. What will payments be?

User Lacey
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To calculate the payments for both scenarios, we need to consider the interest rate, loan amount, and loan term. Let's break down each part:

a. If the borrower makes interest-only payments for 3 years:

The loan amount is $212,000, the start rate is 5 percent, and the loan term is 30 years. However, during the initial 3 years, the borrower only needs to make interest-only payments.

To calculate the monthly payment, we can use the following formula for an interest-only loan:

Monthly Payment = (Loan Amount * Interest Rate) / 12

Monthly Payment = ($212,000 * 0.05) / 12

Monthly Payment = $8,833.33

Therefore, the monthly payments for the first 3 years, during the interest-only period, will be $8,833.33.

b. At the end of year 3, when the reset rate is 6 percent:

After 3 years, the reset rate increases to 6 percent, and the borrower must now make payments to fully amortize the loan over the remaining term.

To calculate the monthly payment for a fully amortizing loan, we can use the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 6% / 12

Monthly Interest Rate = 0.06 / 12

Monthly Interest Rate = 0.005

Next, we calculate the total number of payments remaining, considering the original loan term of 30 years minus the initial 3 years:

Number of Payments = Remaining Years * 12

Number of Payments = (30 - 3) * 12

Number of Payments = 27 * 12

Number of Payments = 324

Now we can calculate the monthly payment:

Monthly Payment = ($212,000 * 0.005) / (1 - (1 + 0.005)^(-324))

Monthly Payment = $1,063.51

Therefore, after the reset rate at the end of year 3, the borrower's monthly payments will be $1,063.51 in order to fully amortize the loan over the remaining 27 years.

User Lee Campbell
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