Suppose you want to buy a $146,000 home. You found a bank that offers a 30-year loan at 5.1% APR. What will be your monthly payment? (Round to the nearest cent.) How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.) Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.) 5 How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.) How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)

We can solve this problem using the **amortization formula** for monthly payments on a fixed-rate mortgage loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount.
- $ 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).

We are given:
- **Loan amount (P):** $146,000
- **Annual interest rate (APR):** 5.1% (so, monthly interest rate $ r = \frac{5.1\%}{12} = \frac{0.051}{12} $)
- **Loan term for the first scenario:** 30 years, so $ n = 30 \times 12 = 360 $ months.
- **Loan term for the second scenario:** 25 years, so $ n = 25 \times 12 = 300 $ months.

Let's calculate the monthly payments for both 30 years and 25 years, and determine the total cost and savings. I'll compute this now.Here are the results:

1. **Monthly payment for a 30-year loan:** $792.71
2. **Total amount paid after 30 years:** $285,374.40
3. **Monthly payment for a 25-year loan:** $862.03
4. **Total amount paid after 25 years:** $258,608.81
5. **Savings by reducing the loan term to 25 years:** $26,765.59

Would you like more details on these calculations or any clarification?

### Related Questions:
1. How is the amortization formula derived?
2. What factors affect mortgage rates?
3. How would making extra payments reduce the loan term or interest?
4. What is the impact of refinancing on monthly payments?
5. How does APR differ from APY (Annual Percentage Yield)?

### Tip:  
Reducing the loan term increases the monthly payment but significantly reduces the total interest paid over time.

Suppose you want to buy a $146,000 home. You found a bank that offers a 30-year loan at 5.1% APR. What will be your monthly payment? (Round to the nearest cent.) How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.) Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.) How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.) How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)

Find out how to calculate the monthly mortgage payment for a $146,000 home loan at 5.1% APR over 30 years, and compare it with a 25-year loan. Learn about amortization, interest rate impact, and how reducing the loan term can save you $26,765.59. Suitable for Grades 11-12.

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