An interest-only ARM is made for $204,000 for 30 years. The start rate is 5 percent, and the borrower will make monthly interest-only payments for three years. Payments thereafter must be sufficient to fully amortize the loan at maturity.

Required:
If the borrower makes interest-only payments for three years, what will the payments be?
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 the payments be?


We will break the problem into two parts: 

1. **Interest-only payments for the first three years.**
2. **Amortized payments after the reset at the end of the third year.**

### Step 1: Interest-Only Payments for the First 3 Years

For an interest-only mortgage, the borrower only pays the interest, not the principal. The interest payment is calculated as follows:

\[
\text{Interest Payment} = \frac{\text{Loan Amount} \times \text{Interest Rate}}{\text{Number of Periods per Year}}
\]

- Loan Amount: $ \$204,000 $
- Annual Interest Rate: $ 5\% = 0.05 $
- Number of Payments per Year: 12 (monthly payments)

So the monthly interest-only payment is:

\[
\text{Interest Payment} = \frac{204,000 \times 0.05}{12}
\]

Let’s calculate this.

\[
\text{Interest Payment} = \frac{204,000 \times 0.05}{12} = \frac{10,200}{12} = 850
\]

Thus, the borrower makes **monthly interest-only payments of $850** for the first three years.

### Step 2: Amortized Payments After the 3rd Year (at 6% Interest Rate)

At the end of year 3, the borrower will switch to an amortizing loan at a reset interest rate of 6%, and will need to fully amortize the loan over the remaining 27 years (30 years - 3 years).

To calculate the monthly payment required to fully amortize the loan, we use the amortization formula:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ = Monthly payment
- $ P $ = Loan amount (\$204,000)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments (27 years × 12 months = 324 payments)

First, convert the 6% annual interest rate into a monthly interest rate:

\[
r = \frac{6\%}{12} = \frac{0.06}{12} = 0.005
\]

Now, let's plug the values into the formula:

\[
M = 204,000 \times \frac{0.005(1 + 0.005)^{324}}{(1 + 0.005)^{324} - 1}
\]

Let me calculate this for you.The monthly payment required to fully amortize the loan after the reset at the end of the third year, with a 6% interest rate, is approximately **$1,272.93**.

### Summary:
1. For the first 3 years, the borrower makes **interest-only payments of $850** per month.
2. After the reset at the end of year 3, the borrower will need to make **fully amortized payments of $1,272.93** per month for the remaining 27 years.

Would you like further clarification or details on any part of the calculation?

Here are 5 related questions:
1. How is the amortization schedule calculated in such loans?
2. What happens if the interest rate resets higher than expected?
3. How would the payments change if the loan term were different?
4. Can the borrower refinance after the interest-only period?
5. What is the risk of an adjustable-rate mortgage (ARM) compared to a fixed-rate mortgage?

**Tip:** Always review the terms of an adjustable-rate mortgage carefully, especially the reset periods and caps on interest rate changes.

An interest-only ARM is made for $204,000 for 30 years. The start rate is 5 percent, and the borrower will make monthly interest-only payments for three years. Payments thereafter must be sufficient to fully amortize the loan at maturity. If the borrower makes interest-only payments for three years, what will the payments be? 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 the payments be?

Learn how to calculate the monthly payments for a $204,000 interest-only adjustable-rate mortgage (ARM) with a 5% start rate and a 6% reset rate after 3 years. Discover how to use the amortization formula to determine payments needed to fully amortize the loan over 27 years.

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