Principal loan amount 
P
=
433600
P= (this appears to be a typo, let's correct this to a more likely figure, say 
Annual interest rate = 8.5% compounded monthly and repayed monthly.
Loan term = 25 years. find the monthly repayment?

Thank you for confirming the loan details. To calculate the monthly payment for a loan of $ P = 433,600 $ with an annual interest rate of 8.5% compounded monthly over 25 years, we use the formula for monthly payments on an amortizing loan:

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

where:

- $ M $ is the monthly payment.
- $ P $ is the principal loan amount ($ P = 433,600 $).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (number of years times 12 for monthly payments).

### Step-by-Step Calculation

1. **Convert the annual interest rate to a monthly interest rate:**

   \[
   r = \frac{8.5\%}{12} = \frac{0.085}{12} \approx 0.0070833
   \]

2. **Convert the number of years to the number of months:**

   \[
   n = 25 \times 12 = 300 \text{ months}
   \]

3. **Plug these values into the monthly payment formula:**

   \[
   M = 433,600 \cdot \frac{0.0070833 \cdot (1+0.0070833)^{300}}{(1+0.0070833)^{300} - 1}
   \]

### Calculation

1. Calculate $(1 + r)^n$:

   \[
   (1 + 0.0070833)^{300} \approx 7.212
   \]

2. Calculate the numerator $ r \cdot (1+r)^n $:

   \[
   0.0070833 \times 7.212 \approx 0.05112
   \]

3. Calculate the denominator $(1+r)^n - 1$:

   \[
   7.212 - 1 = 6.212
   \]

4. Calculate the monthly payment $ M $:

   \[
   M = 433,600 \times \frac{0.05112}{6.212} \approx 433,600 \times 0.00823 \approx 3,569.65
   \]

Thus, the monthly payment is approximately **$3,569.65**.

### Summary

- **Monthly payment (M)**: $3,569.65
- **Loan term**: 25 years (300 months)
- **Interest rate**: 8.5% per annum, compounded monthly

Would you like further details or have any questions about this calculation?

### Related Questions

1. What is the total amount paid over the entire loan period, including interest?
2. How much of the monthly payment goes toward principal and interest in the first month?
3. How does an increase in the interest rate to 9% affect the monthly payment?
4. What would the monthly payment be if the loan term was reduced to 20 years?
5. How would making an extra monthly payment of $500 impact the total interest paid over the life of the loan?

### Tip

When dealing with loans, always consider the option of making extra payments toward the principal. This can reduce the total interest paid and shorten the loan term, saving money in the long run.

Learn how to calculate the monthly repayment for a $433,600 loan with an annual interest rate of 8.5% compounded monthly over 25 years. Understand the formula used and follow a step-by-step calculation to find out the monthly payment.

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