$12,849.32
The total cost of the boat will be the down payment on the boat plus the total amount of the payments on the loan made for the boat. The down payment is given as $875, and the loan amount is $8880. The formula for determining what each payment of a loan should be is:
P = r(PV)/(1-(1+r)^(-n))
where
P = Payment per period
r = Interest rate per period
n = number of periods
PV = present value
Since there isn't any mention of whether the loan is being paid in monthly or yearly installments, I'm going to guess and assume yearly payments. So substitute the known values into the formula and solve:
P = 0.104(8880)/(1 - (1+0.104)^(-6))
P = 923.52/(1 - 1.104^(-6))
P = 923.52/(1 - 0.552313374)
P = 923.52/0.447686626
P = 2062.871541
And since 6 payments are made, plus the down payment, the total cost is
2062.87 * 6 + 875 = 13252.22
Looking at the available answers, none of them come close and in fact all of them are lower than the calculated payment. This indicates that the assumption of yearly payments is in error and it's more likely that monthly payments are being made instead. So instead of 6 payment periods, there will be 6*12 = 72 payment periods and the interest per period will be 10.4%/12 = 0.866666667%. Substituting the new values into the formula and solving gives:
P = 0.00866666667(8880)/(1-(1+0.00866666667)^(-72))
P =76.96/(1-(1.00866666667)^(-72))
P =76.96/(1-0.537239374)
P =76.96/0.462760626
P = 166.31
So each monthly loan payment is $166.31 and the total cost now is:
72 * 166.31 + 875 = 12849.32
And since 12849.32 matches the choice of $12,849.32, that is the total cost of the boat after 6 years.
