QuestionJuly 26, 2025

A sailboat costs 31,503 You pay 20% down and amortize the rest with equal monthly payments over a 13-year period. If you must pay 6.6% compounded monthly, what is your monthly payment? How much interest will you pay? Monthly payments: Ssquare (Round to two decimal places.)

A sailboat costs 31,503 You pay 20% down and amortize the rest with equal monthly payments over a 13-year period. If you must pay 6.6% compounded monthly, what is your monthly payment? How much interest will you pay? Monthly payments: Ssquare (Round to two decimal places.)
A sailboat costs 31,503 You pay 20% down and amortize the rest with equal monthly payments over a 13-year period. If you must pay 6.6% compounded monthly, what is your monthly payment? How much interest will you pay? Monthly payments: Ssquare (Round to two decimal places.)

Solution
4.2(240 votes)

Answer

Monthly Payment: \243.96; Total Interest Paid: \12,859.36 Explanation 1. Calculate Down Payment The down payment is 20\% of the sailboat's cost. Calculate it as 0.20 \times 31,503 = 6,300.60. 2. Determine Loan Amount Subtract the down payment from the total cost to find the loan amount: 31,503 - 6,300.60 = 25,202.40. 3. Calculate Monthly Interest Rate Convert annual interest rate to monthly: \frac{6.6\%}{12} = 0.55\% or 0.0055 in decimal form. 4. Calculate Number of Payments Multiply the number of years by 12 months/year: 13 \times 12 = 156 payments. 5. Use Amortization Formula for Monthly Payment **Monthly Payment Formula**: M = P \frac{r(1+r)^n}{(1+r)^n-1} where P = 25,202.40, r = 0.0055, and n = 156. Substitute values: M = 25,202.40 \frac{0.0055(1+0.0055)^{156}}{(1+0.0055)^{156}-1}. 6. Calculate Monthly Payment Compute using the formula: M \approx 243.96. 7. Calculate Total Payment Over Loan Period Multiply monthly payment by number of payments: 243.96 \times 156 = 38,061.76. 8. Calculate Total Interest Paid Subtract principal from total payment: 38,061.76 - 25,202.40 = 12,859.36.

Explanation

1. Calculate Down Payment<br /> The down payment is $20\%$ of the sailboat's cost. Calculate it as $0.20 \times 31,503 = 6,300.60$.<br /><br />2. Determine Loan Amount<br /> Subtract the down payment from the total cost to find the loan amount: $31,503 - 6,300.60 = 25,202.40$.<br /><br />3. Calculate Monthly Interest Rate<br /> Convert annual interest rate to monthly: $\frac{6.6\%}{12} = 0.55\%$ or $0.0055$ in decimal form.<br /><br />4. Calculate Number of Payments<br /> Multiply the number of years by 12 months/year: $13 \times 12 = 156$ payments.<br /><br />5. Use Amortization Formula for Monthly Payment<br /> **Monthly Payment Formula**: $M = P \frac{r(1+r)^n}{(1+r)^n-1}$ where $P = 25,202.40$, $r = 0.0055$, and $n = 156$.<br /> Substitute values: $M = 25,202.40 \frac{0.0055(1+0.0055)^{156}}{(1+0.0055)^{156}-1}$.<br /><br />6. Calculate Monthly Payment<br /> Compute using the formula: $M \approx 243.96$.<br /><br />7. Calculate Total Payment Over Loan Period<br /> Multiply monthly payment by number of payments: $243.96 \times 156 = 38,061.76$.<br /><br />8. Calculate Total Interest Paid<br /> Subtract principal from total payment: $38,061.76 - 25,202.40 = 12,859.36$.
Click to rate:

Similar Questions