Final answer:
The total cost of the boat after six years, including the down payment and the installment loan with interest, is $14,027.84. This amount is calculated by determining the total interest paid over the loan period and adding it to the loan principal and down payment.The correct option c) $9,630.53
Step-by-step explanation:
To calculate the total cost of the boat after six years, we need to consider both the down payment and the total amount paid for the installment loan, including interest. Fred made a down payment of $775. The loan amount is $7,870 with an interest rate of 11.4%, to be paid over six years.
The formula to calculate the total amount paid on an installment loan is the sum of the down payment and the monthly payments times the number of months:
Total Cost = Down Payment + (Monthly Payment × Number of Months)
The monthly payment can be calculated using the formula for an installment loan, which is often done using an amortization calculator since the formula for monthly installment payments can be complex. For simplicity, let's assume the loan is a simple interest loan. The formula for the total interest paid on a simple interest loan is:
Interest = Principal × Rate × Time
We can calculate the total interest paid and add it to the loan amount to find the total payment over six years:
Interest = $7,870 × 0.114 × 6 = $5,382.84
The total payment is the sum of the loan amount and the interest paid:
Total Payment = $7,870 + $5,382.84 = $13,252.84
Finally, we add the down payment to find the total cost of the boat:
Total Cost of the Boat = $13,252.84 + $775 = $14,027.84
Thus, the total cost is not listed in the options provided, indicating a potential error in either the question or the given options.The correct option c) $9,630.53