Questions: Example 2: Jasyn plans to buy a house. He has saved 25,000 for a down payment and plans to finance 175,000. His bank offers a 30 -year fixed rate loan at 4.25% and a 5 / 1 ARM at 3.5%. Fill in the missing values How much does he owe on the house at the end of year 5 (or after 60 payments) (a) if he chooses the 30-year fixed? (b) if he choosed the 5 / 1 ARM?

Solution Steps

To solve this problem, we need to calculate the remaining balance on the mortgage after 5 years (or 60 payments) for both the 30-year fixed-rate loan and the 5/1 ARM. This involves using the formula for the remaining balance on a loan, which takes into account the principal, interest rate, and number of payments made. For the 5/1 ARM, we assume the interest rate remains constant for the first 5 years.

To find the monthly payment for the 30-year fixed-rate loan, we use the formula for the monthly payment of an amortizing loan:

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

where:

• \( M \) is the monthly payment,
• \( P = 175,000 \) is the principal,
• \( r = \frac{0.0425}{12} \) is the monthly interest rate,
• \( n = 30 \times 12 = 360 \) is the total number of payments.

The remaining balance after 60 payments is calculated using the formula:

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

where:

• \( B \) is the remaining balance,
• \( p = 60 \) is the number of payments made.

Substituting the values, we find:

\[ B \approx 158,913.4690 \]

For the 5/1 ARM, the monthly payment is calculated similarly, with:

• \( r = \frac{0.035}{12} \).

Using the same formula for the remaining balance, we substitute the ARM values:

\[ B \approx 156,969.8772 \]

Final Answer