Dr. & Mr. Wilson were delighted to find a house for sale that they loved which required them to borrow $160,000. They need to decide between a 20-year or 30-year loan. Both loans charge interest at a rate of 9.6% per year compounded monthly.
20-year Loan
(a.) Find the monthly payments for the 20-year loan.

To calculate the monthly payment for the 20-year loan, we can use the formula for the monthly payment on an amortized loan:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal (the amount borrowed) = \$160,000
- $ r $ = monthly interest rate (annual rate divided by 12)
- $ n $ = total number of payments (loan term in years multiplied by 12)

Given:
- Annual interest rate = 9.6% = 0.096
- Loan term = 20 years
- Monthly interest rate $ r = \frac{9.6\%}{12} = \frac{0.096}{12} = 0.008 $
- Total number of payments $ n = 20 \times 12 = 240 $

Let's compute the monthly payment using these values.The monthly payment for the 20-year loan would be approximately **$1,501.87**.

Do you have any questions or would you like further details on this?

Here are 5 related questions to consider:
1. How much interest will be paid over the life of the 20-year loan?
2. How do monthly payments differ if the loan term is increased to 30 years?
3. How does a change in interest rate affect monthly payments?
4. What is the total cost of the house with interest included for the 20-year loan?
5. What is the benefit of paying off a loan in 20 years versus 30 years?

**Tip:** Making extra payments on a loan can significantly reduce the total interest paid over the life of the loan.

Find out how to calculate the monthly payments for a 20-year loan of $160,000 with a 9.6% annual interest rate compounded monthly. This solution explains the use of the amortized loan payment formula, key mathematical concepts, and provides a detailed step-by-step calculation.

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