To determine the monthly payment and total interest paid on the sailboat loan, we need to follow these steps:

1. Calculate the down payment.
2. Determine the loan amount.
3. Calculate the monthly payment using the loan amortization formula.
4. Calculate the total amount paid over the life of the loan.
5. Determine the total interest paid.

Step 1: Calculate the Down Payment

The down payment is 5% of the total cost of the sailboat.

$\text{Down Payment} = 0.05 \times 29135$

$\text{Down Payment} = 1456.75$

Step 2: Determine the Loan Amount

The loan amount is the cost of the sailboat minus the down payment.

$\text{Loan Amount} = 29135 - 1456.75$

$\text{Loan Amount} = 27678.25$

Step 3: Calculate the Monthly Payment

We use the formula for the monthly payment on an amortizing loan:

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

where:

• $M$ is the monthly payment,
• $P$ is the principal (loan amount),
• $r$ is the monthly interest rate,
• $n$ is the total number of payments.

Given:

• $P = 27678.25$
• Annual interest rate = 8.4%, so monthly interest rate $r = \frac{8.4\%}{12} = 0.007$
• $n = 8 \times 12 = 96$ months

Plugging in these values:

$M = 27678.25 \frac{0.007(1+0.007)^{96}}{(1+0.007)^{96} - 1}$

First, calculate $(1+0.007)^{96}$:

$(1+0.007)^{96} \approx 1.854$

Then, the formula becomes:

$M = 27678.25 \frac{0.007 \times 1.854}{1.854 - 1}$

$M = 27678.25 \frac{0.012978}{0.854}$

$M = 27678.25 \times 0.01519$

$M \approx 420.28$

So, the monthly payment is approximately $\$420.28$.

Step 4: Calculate the Total Amount Paid

$\text{Total Amount Paid} = M \times n$

$\text{Total Amount Paid} = 420.28 \times 96$

$\text{Total Amount Paid} \approx 40346.88$

Step 5: Determine the Total Interest Paid

$\text{Total Interest Paid} = \text{Total Amount Paid} - \text{Loan Amount}$

$\text{Total Interest Paid} = 40346.88 - 27678.25$

$\text{Total Interest Paid} \approx 12668.63$

Summary

• Monthly Payment: $\$420.28$
• Total Interest Paid: $\$12668.63$

Would you like more details or have any questions?

Here are 5 relative questions that expand on this information:

1. How would the monthly payment change if the interest rate were 7% instead of 8.4%?
2. What would be the monthly payment for a 10-year loan term at the same interest rate?
3. How much would you save in interest if you made an additional monthly payment of $100?
4. What is the impact of increasing the down payment to 10% on the monthly payment and total interest paid?
5. How can you calculate the remaining loan balance after 4 years of payments?

Tip: Regularly paying a little extra towards the principal can significantly reduce the total interest paid over the life of the loan.