A sailboat costs $ 28 comma 755. You pay 10 % down and amortize the rest with equal monthly payments over a 8​-year period. If you must pay 7.5 % compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?
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Part 1
Monthly​ payments: ​$
  
enter your response here ​(Round to two decimal​ places.)

Let's break down the problem into steps to find the monthly payment and the total interest paid.

### 1. **Down Payment**:
You pay 10% down for the sailboat. 
The total cost of the sailboat is $28,755. So, the down payment is:

\[
\text{Down Payment} = 0.10 \times 28,755 = 2,875.50
\]

### 2. **Loan Amount**:
The remaining amount to be financed is:

\[
\text{Loan Amount} = 28,755 - 2,875.50 = 25,879.50
\]

### 3. **Loan Parameters**:
- Loan Amount: $25,879.50
- Annual Interest Rate: 7.5%
- Number of years: 8
- Monthly interest rate (since it is compounded monthly):

\[
r = \frac{7.5\%}{12} = \frac{0.075}{12} = 0.00625
\]

- Total number of payments (since the loan is over 8 years, with monthly payments):

\[
n = 8 \times 12 = 96 \text{ months}
\]

### 4. **Monthly Payment Formula**:
The monthly payment formula for an amortized loan is:

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

Where:
- $M$ = monthly payment
- $P$ = loan amount
- $r$ = monthly interest rate
- $n$ = total number of payments

Now, we can plug in the values:

\[
M = \frac{25,879.50 \times 0.00625}{1 - (1 + 0.00625)^{-96}}
\]

Let me calculate that for you.The monthly payment is approximately **$359.31**.

### 5. **Total Interest Paid**:
To calculate the total interest paid over the loan period, we can first find the total amount paid over the 96 months and then subtract the principal (loan amount).

\[
\text{Total Payment} = M \times n = 359.31 \times 96
\]
\[
\text{Interest Paid} = \text{Total Payment} - \text{Loan Amount}
\]

Let me calculate the interest for you.The total interest paid over the 8-year period is approximately **$8,614.03**.

### Summary:
- **Monthly Payment**: $359.31
- **Total Interest Paid**: $8,614.03

Would you like more details on the calculation or have any other questions?

Here are 5 related questions you might find helpful:
1. How would the monthly payment change if the interest rate was lower, say 5%?
2. How would a longer repayment period, like 10 years, affect the monthly payment?
3. What happens if you increase the down payment percentage?
4. How can I calculate the remaining loan balance after a certain number of payments?
5. How is interest affected by paying extra towards the principal each month?

**Tip:** Making extra payments toward the principal can significantly reduce the total interest you pay over the life of the loan!

A sailboat costs $28,755. You pay 10% down and amortize the rest with equal monthly payments over an 8-year period. If you must pay 7.5% compounded monthly, what is your monthly payment? How much interest will you pay?

Calculate the monthly payment and total interest for a sailboat costing $28,755 with a 10% down payment, amortized over 8 years at 7.5% compounded monthly. Learn the amortization formula and interest breakdown for accurate financial planning.

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