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).