Gerritt wants to buy a car that costs $26,750. The interest rate on his loan is 5.33 percent compounded monthly and the loan is for 7 years. What are his monthly payments?

Multiple Choice

$382.24

$380.55

$401.36

$369.50

$389.86

To calculate Gerritt's monthly payments, we can use the formula for monthly payments on a loan with compound interest:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal ($26,750)
- $ r $ = monthly interest rate (annual rate / 12)
- $ n $ = total number of payments (years * 12)

### Step 1: Identify values
- Loan principal $ P = 26,750 $
- Annual interest rate = 5.33%, so monthly interest rate $ r = \frac{5.33\%}{12} = \frac{0.0533}{12} = 0.0044417 $
- Loan term = 7 years, so total number of payments $ n = 7 \times 12 = 84 $

### Step 2: Substitute into the formula

\[
M = \frac{26750 \cdot 0.0044417 \cdot (1 + 0.0044417)^{84}}{(1 + 0.0044417)^{84} - 1}
\]

I'll calculate this next.Gerritt's monthly payment comes out to approximately **$382.24**.

Thus, the correct answer is:

\[
\boxed{382.24}
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions to consider:
1. How does the loan term affect monthly payments?
2. What happens if the interest rate is compounded quarterly instead of monthly?
3. How would extra monthly payments impact the loan balance?
4. What would Gerritt's monthly payment be with a shorter loan term, such as 5 years?
5. How much total interest would Gerritt pay over the life of the loan?

**Tip:** The longer the loan term, the smaller the monthly payments, but the total interest paid over time increases.

Gerritt wants to buy a car that costs $26,750. The interest rate on his loan is 5.33 percent compounded monthly and the loan is for 7 years. What are his monthly payments? Multiple Choice: $382.24, $380.55, $401.36, $369.50, $389.86.

Learn how to calculate monthly payments for a $26,750 car loan with an interest rate of 5.33% compounded monthly over a loan term of 7 years. Using the loan payment formula, determine Gerritt's monthly payment to be $382.24. This problem involves compound interest and monthly payment calculations, suitable for Grades 10-12.

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