Find the monthly payment needed to amortize principal and interest for the fixed-rate mortgage.
Use either the regular monthly payment formula or the given table. Loan amount is $116,000. Interest rate is 6.5%. term is 20 years. What is the monthly payment.

To find the monthly payment needed to amortize the principal and interest for the fixed-rate mortgage, we use the following 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 (\$116,000)
- $r$ is the monthly interest rate (annual rate divided by 12)
- $n$ is the total number of payments (loan term in years multiplied by 12)

Given:
- Loan amount, $P = \$116,000$
- Annual interest rate = 6.5%
- Monthly interest rate, $r = \frac{6.5\%}{12} = \frac{0.065}{12} \approx 0.005417$
- Loan term = 20 years
- Total number of payments, $n = 20 \times 12 = 240$

Plugging these values into the formula:

\[
M = 116{,}000 \times \frac{0.005417(1+0.005417)^{240}}{(1+0.005417)^{240} - 1}
\]

First, compute $ (1 + r)^n $:

\[
(1 + 0.005417)^{240} \approx 3.52499
\]

Next, calculate the numerator:

\[
0.005417 \times 3.52499 \approx 0.019093
\]

Then, calculate the denominator:

\[
3.52499 - 1 = 2.52499
\]

Now, compute the fraction:

\[
\frac{0.019093}{2.52499} \approx 0.007562
\]

Finally, multiply by the loan amount:

\[
M = 116{,}000 \times 0.007562 \approx 877.19
\]

Thus, the monthly payment for the mortgage is approximately \$877.19.

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

Here are 8 related questions to expand on this information:
1. How would the monthly payment change if the interest rate was 5.5% instead of 6.5%?
2. What is the total interest paid over the life of the loan?
3. How much principal is paid off after 5 years?
4. What would be the monthly payment for a 30-year mortgage at the same interest rate?
5. How does the monthly payment change if the loan amount is increased to \$150,000?
6. What is the impact on monthly payments if the loan term is reduced to 15 years?
7. How much interest is paid in the first year of the mortgage?
8. What is the outstanding principal after 10 years of payments?

**Tip:** Use an online mortgage calculator or financial software to easily compute monthly payments and generate amortization schedules for various loan scenarios.

Learn how to calculate the monthly payment needed to amortize a $116,000 loan at 6.5% interest over 20 years. Use the fixed-rate mortgage payment formula with detailed step-by-step calculations.

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