Suppose you want to buy a $145,000 home. You found a bank that offers a 30-year loan at 3.7% 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.)

$

To find the monthly payments and total amounts paid to the bank for different loan terms, we will use the same loan payment formula:

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

where:

- $ M $ is the monthly payment.
- $ P = 145,000 $ is the principal amount (home price).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments.

**1. Monthly Payment for a 30-Year Loan:**

Given:
- Annual interest rate = 3.7%, so $ r = \frac{3.7\%}{12} = 0.0030833 $.
- Loan term = 30 years, so $ n = 30 \times 12 = 360 $.

Let's calculate the monthly payment and total amount paid over 30 years.

**2. Monthly Payment for a 25-Year Loan:**

Given:
- The same interest rate of 3.7%, so $ r = 0.0030833 $.
- Loan term = 25 years, so $ n = 25 \times 12 = 300 $.

We'll calculate the monthly payment and the total amount paid over 25 years, and then find the savings.Here are the calculations based on the given conditions:

1. **Monthly payment for the 30-year loan**: \$667.41
2. **Total amount paid to the bank over 30 years**: \$240,267.72
3. **Monthly payment for the 25-year loan**: \$741.55
4. **Total amount paid to the bank over 25 years**: \$222,464.98
5. **Savings by reducing the mortgage loan term to 25 years**: \$17,802.73

Would you like more details or have any questions? Here are some related topics:

1. What would the monthly payment be for a different interest rate?
2. How does making extra payments affect the total interest paid?
3. What would be the effect of a larger down payment on the loan terms?
4. How do bi-weekly payments compare to monthly payments for savings?
5. What happens if the interest rate increases during the loan period?

**Tip:** Shortening the loan term often results in significant savings on interest, even though the monthly payments are higher.

Explore how to calculate monthly mortgage payments and savings using a 30-year and 25-year loan example. Understand the impact of loan term reduction on total payments. Includes detailed calculations and savings analysis.

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