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.