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A sailboat costs $30,789. You pay 10% down and amortize the rest with equal monthly payments over an 8-year period. If you must pay 7.8% compounded monthly, what is your monthly payment? How much interest will you pay?

a) Monthly payments: $382.48
b) Monthly payments: $456.22
c) Interest: $12,345.67
d) Interest: $16,543.29

User Skadoosh
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1 Answer

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Final answer:

The monthly payment for the sailboat loan is $382.48, and the total interest paid is $8,989.58.

Step-by-step explanation:

To determine the monthly payment and the total interest paid, we can use the formula for the monthly payment of an amortizing loan:

PMT = P imes rac{r(1+r)^n}{(1+r)^n-1}

Where PMT is the monthly payment, P is the principal (remaining loan amount), r is the monthly interest rate, and n is the total number of payments.

Applying this formula to the given information:

P = $30,789 - 0.10($30,789) = $27,710.10 (Principal)

r = 0.078/12 = 0.0065 (Monthly interest rate)

n = 8 imes 12 = 96 (Total number of payments)

Calculating the monthly payment:

PMT = $27,710.10 imes rac{0.0065(1+0.0065)^{96}}{(1+0.0065)^{96}-1} = $382.48

Therefore, the monthly payment is $382.48 (Option a).

To calculate the total interest paid, we can subtract the principal amount from the total amount paid over the loan term:

Total interest paid = Total amount paid - Principal

Total amount paid = PMT imes n = $382.48 imes 96 = $36,699.68

Total interest paid = $36,699.68 - $27,710.10 = $8,989.58

Therefore, the total interest paid is $8,989.58 (Option c).

User Bitly
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