To solve this problem, we'll follow two steps:

1. Find the monthly payment using the loan amortization formula.
2. Calculate the total interest paid over the loan period.

Step 1: Calculate the Monthly Payment

The formula for calculating the monthly payment on an amortized loan is:

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

Where:

• $M$ is the monthly payment.
• $P$ is the loan principal (amount to be financed).
• $r$ is the monthly interest rate (annual rate divided by 12).
• $n$ is the total number of payments (months).

Information from the problem:

• The total cost of the sailboat is $27,661.
• You pay 15% down, so the down payment is $27,661 \times 0.15 = 4,149.15$.
• The loan principal is $27,661 - 4,149.15 = 23,511.85$.
• The annual interest rate is 6.9% compounded monthly, so the monthly interest rate is $\frac{6.9}{12} = 0.575\%$, or $0.00575$ as a decimal.
• The loan period is 12 years, which gives $n = 12 \times 12 = 144$ months.

Now, let's calculate the monthly payment using this formula.

Step 2: Calculate the Total Interest Paid

Once we find the monthly payment, the total interest can be found by calculating the difference between the total amount paid over the life of the loan and the loan principal:

$\text{Total Interest} = (M \times n) - P$

Let me compute these values for you.The monthly payment for the sailboat will be approximately $240.54.

The total interest paid over the 12-year period will be approximately $11,125.90.

Would you like further details or clarification on how these values were calculated? Here are some related questions to consider:

1. How would the monthly payment change if the interest rate was lower?
2. What happens to the total interest paid if the loan term is shorter?
3. How would an increased down payment affect the monthly payment?
4. Can I use the same formula for other types of loans?
5. How do early repayments impact the total interest paid?

Tip: A larger down payment reduces both the loan amount and the total interest paid over time.