A sailboat costs $17,079. You pay 30% down and amortize the rest with equal monthly payments over a 66​-year period. If you must pay 8.7% compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?

To solve this problem, we need to calculate two things:

1. **Monthly Payment** using the amortization formula.
2. **Total Interest Paid** over the loan period.

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### Step 1: Calculate the Down Payment
The down payment is 30% of the sailboat's cost:

\[
\text{Down Payment} = 0.30 \times 17,079 = 5,123.70
\]

So, the amount you need to finance (the loan principal) is:

\[
\text{Principal (P)} = 17,079 - 5,123.70 = 11,955.30
\]

### Step 2: Identify Variables for the Loan Amortization Formula
The loan amortization formula is:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (\$11,955.30).
- $ r $ is the monthly interest rate (8.7% annual, compounded monthly, so $ \frac{8.7\%}{12} $).
- $ n $ is the total number of payments (66 years × 12 months per year).

### Step 3: Calculate Monthly Interest Rate and Total Number of Payments
- Monthly interest rate $ r = \frac{8.7\%}{12} = 0.00725 $ (or 0.0087/12).
- Total number of payments $ n = 66 \times 12 = 792 $.

### Step 4: Calculate the Monthly Payment
Now we can substitute these values into the amortization formula to calculate the monthly payment. I'll do the calculation.The monthly payment for the sailboat will be approximately **$86.96**.

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### Step 5: Calculate the Total Interest Paid

To calculate the total interest, we need to find the total amount paid over the 66-year period and subtract the principal.

- **Total amount paid** = Monthly payment × Total number of payments
- **Interest paid** = Total amount paid - Principal

Let me calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the total interest paid using the following method:

1. **Total amount paid**: Multiply the monthly payment (\$86.96) by the total number of payments (792).
2. **Total interest**: Subtract the original loan amount (\$11,955.30) from the total amount paid to get the interest paid.

Would you like further assistance or any clarification on these steps?

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Here are five related questions for further practice:
1. How does the length of the loan term affect the total interest paid?
2. What happens if the interest rate is compounded annually instead of monthly?
3. How would the monthly payment change if the interest rate was reduced by 1%?
4. What is the impact of increasing the down payment on the total interest paid?
5. How would you calculate the future value of this loan?

**Tip:** The longer your loan term, the more interest you will pay overall, even though the monthly payment might be smaller.

A sailboat costs $17,079. You pay 30% down and amortize the rest with equal monthly payments over a 66-year period. If you must pay 8.7% compounded monthly, what is your monthly payment? How much interest will you pay?

Calculate the monthly payment and total interest for a sailboat loan with a 30% down payment and 8.7% interest compounded monthly over 66 years. Using the loan amortization formula, this detailed guide covers interest rates, principal, and total interest paid.

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