To calculate the monthly payment needed to amortize the loan, we use the formula for a fixed-rate mortgage:

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

Where:

• $M$ is the monthly payment.
• $P$ is the loan amount ($160,000).
• $r$ is the monthly interest rate (annual interest rate divided by 12).
• $n$ is the total number of payments (loan term in years × 12).

Step 1: Calculate the monthly interest rate

$r = \frac{9.3\%}{12} = 0.093 / 12 = 0.00775$

Step 2: Calculate the total number of payments

$n = 25 \times 12 = 300$

Step 3: Substitute into the formula

$M = 160,000 \cdot \frac{0.00775(1 + 0.00775)^{300}}{(1 + 0.00775)^{300} - 1}$

Step 4: Compute the values

• $(1 + 0.00775) = 1.00775$
• $(1.00775)^{300} \approx 9.12855$
• $0.00775 \cdot 9.12855 \approx 0.07068926$
• $9.12855 - 1 \approx 8.12855$
• $\frac{0.07068926}{8.12855} \approx 0.0086947$

Finally: $M = 160,000 \cdot 0.0086947 = 1,391.15$

Monthly Payment:

The monthly payment is approximately $1,391.15.

Would you like to verify this calculation with another method, or do you need more details?

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Related Questions:

1. How does the interest rate affect the monthly payment for the same loan amount and term?
2. What would the monthly payment be if the loan term were 30 years instead of 25 years?
3. What portion of the first payment goes toward interest versus principal?
4. How much total interest will be paid over the life of this loan?
5. Can prepayments significantly reduce the total interest paid? If so, how?

Tip:

For faster calculations, consider using financial calculators or online tools that automate this formula for any loan scenario.