A sailboat costs 

$ 21 comma 835$21,835. 

You pay 

25 %25% 

down and amortize the rest with equal monthly payments over a 

88​-year 

period. If you must pay 

7.2 %7.2% 

compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?

Question content area bottom

Part 1

Monthly​ payments: 

​$enter your response here 

​(Round to two decimal​ places.)




To solve this problem, we will follow the same steps as before but with the updated values:

1. **Calculate the down payment:** $ 25\% $ of the sailboat's cost.
2. **Calculate the loan amount:** Subtract the down payment from the total cost.
3. **Calculate the monthly payment:** Using the amortizing loan formula.
4. **Calculate the total interest paid.**

Let's compute these values step-by-step.

### 1. Down Payment
The sailboat costs $ \$21,835 $ and the down payment is $ 25\% $.

\[
\text{Down Payment} = 0.25 \times 21835
\]

### 2. Principal Loan Amount
\[
\text{Principal} = \text{Total Cost} - \text{Down Payment}
\]

### 3. Monthly Payment
The annual interest rate is $ 7.2\% $ compounded monthly, so the monthly interest rate $ r $ is:
\[
r = \frac{7.2\%}{12} = 0.006
\]
The loan term is 8 years, so the number of payments $ n $ is:
\[
n = 8 \times 12 = 96
\]

Now, let's calculate these values.### Results

1. **Down Payment:** $5,458.75
2. **Principal Loan Amount:** $16,376.25
3. **Monthly Payment:** $224.90 (rounded to two decimal places)
4. **Total Amount Paid:** $21,590.65
5. **Total Interest Paid:** $5,214.40

Would you like any further details or have any questions?

---

**Related Questions:**

1. What would the monthly payment be if the down payment were only 10%?
2. How would the total interest change if the interest rate were reduced to 6%?
3. What is the effect on the monthly payment if the loan term is extended to 10 years?
4. How is the monthly payment calculated in an amortizing loan?
5. What impact does the down payment have on the overall cost of the loan?
6. How does the length of the loan term affect the total interest paid?
7. What strategies can be used to pay off the loan faster?
8. How can you calculate the remaining loan balance after 5 years?

**Tip:** Making extra payments on the principal can significantly reduce the total interest paid over the life of the loan.

Learn how to calculate monthly payments and total interest for purchasing a sailboat. This problem involves determining the monthly payment using amortization over an 8-year period with a 7.2% annual interest rate compounded monthly. Suitable for Grades 10-12.

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