The Flemings secured a bank loan of $288,000 to help finance the purchase of a house. The bank charges interest at a rate of 3%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)
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This problem involves calculating the monthly mortgage payment on a loan with compounded interest. The formula to determine the monthly payment for an amortizing loan is:

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

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

### Given values:
- $ P = 288,000 $
- Annual interest rate = 3%, so the monthly interest rate is $ r = \frac{3\%}{12} = 0.0025 $
- Loan term = 25 years, so the number of monthly payments is $ n = 25 \times 12 = 300 $

Now, substitute these values into the formula:

\[
M = 288,000 \times \frac{0.0025(1+0.0025)^{300}}{(1+0.0025)^{300} - 1}
\]

Let's compute this step by step.The size of each monthly repayment should be approximately **$1,365.73** to amortize the loan over 25 years.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:
1. How does changing the loan term affect the monthly payment?
2. What would the payment be if the interest rate was higher, say 4%?
3. How much total interest will the Flemings pay over the life of the loan?
4. What is the effect of making extra payments toward the loan principal?
5. How does a fixed-rate mortgage compare with a variable-rate mortgage?

**Tip**: Making additional payments directly toward the principal can significantly reduce the total interest paid over the life of the loan.

The Flemings secured a bank loan of $288,000 to help finance the purchase of a house. The bank charges interest at a rate of 3%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)

Find out how to calculate the monthly repayment amount for a $288,000 mortgage with a 3% annual interest rate, amortized over 25 years. This problem involves key concepts like compound interest and loan amortization, providing a detailed step-by-step solution. Ideal for high school students in Grades 11-12.

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