A company offers a motorboat engine for $40,736.25, including sales tax. If you make a down payment of 20 % and finance the remaining cost at an annual interest rate of 5.7% for 3 years, find the monthly payment.

To determine the monthly payment for financing the boat engine, we need to calculate the amount financed and use the formula for monthly payments on an installment loan.

### Step 1: Calculate the down payment
The down payment is 20% of the total cost.

\[
\text{Down payment} = 0.20 \times 40,736.25 = 8,147.25
\]

### Step 2: Determine the amount financed
The remaining amount to be financed is:

\[
\text{Amount financed} = 40,736.25 - 8,147.25 = 32,589
\]

### Step 3: Use the loan formula
We will use the formula for monthly payments on a loan:

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

Where:
- $ M $ is the monthly payment,
- $ P $ is the amount financed (32,589),
- $ r $ is the monthly interest rate, and
- $ n $ is the number of monthly payments.

Given:
- Annual interest rate = 5.7%, so monthly rate $ r = \frac{5.7}{12 \times 100} = 0.00475 $,
- The loan term is 3 years, so $ n = 3 \times 12 = 36 $ months.

### Step 4: Plug in the values
Now, substituting the values into the formula:

\[
M = \frac{32,589 \cdot 0.00475(1 + 0.00475)^{36}}{(1 + 0.00475)^{36} - 1}
\]

Let me calculate the monthly payment.The monthly payment for the financed amount is approximately **$987.00**.

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How much total interest will be paid over the 3 years?
2. What would the monthly payment be if the interest rate was lower, say 4%?
3. How would the monthly payment change if the loan term was extended to 5 years?
4. What is the total cost of the engine after financing is complete?
5. How does making a larger down payment (e.g., 30%) affect the monthly payment?

**Tip:** Paying extra each month on a loan can reduce the total interest paid over time.

Learn how to calculate the monthly payment for a motorboat engine costing $40,736.25, with a 20% down payment and a 5.7% annual interest rate over 3 years. The detailed solution explains key finance concepts like loan amortization and interest calculation, making it suitable for high school seniors and college students.

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