Question

Ruben bought a boat valued at $16,500 on the installment plan requiring a 12% down payment, and equal monthly payments of $255. If Ruben took out a loan for the amount need after the down payment, at 4.65% compounded quarterly, how long would it take Ruben to pay off the loan? (Give your answer in years and months)

PLEASE POST THE FINANCIAL CALCULATOR NUMERICALS

Answer 1

Ruben would take approximately 6 years and 10 months to pay off the loan.

Step-by-step explanation:

To determine how long it would take Ruben to pay off the loan, we need to calculate the total amount of the loan and then use the monthly payments to find the time period.

The loan amount will be the boat value minus the down payment:

$16,500 - ($16,500 * 12%)

= $16,500 - $1,980

= $14,520.

Now, we can use the formula for the future value of an ordinary annuity:

`FV = P((1 + r/n)^(n*t) - 1)/(r/n),`

where FV is the future value, P is the monthly payment, r is the interest rate, n is the number of compounding periods per year, and t is the time period in years.

In this case, the future value will be the loan amount, P is $255, r is 4.65% (0.0465), n is 4 (compounded quarterly), and we need to solve for t.

Plugging in the values, we get:

`$14,520 = $255((1 + 0.0465/4)^(4*t) - 1)/(0.0465/4).`

By solving this equation, t is approximately 6.8 years or 6 years and 10 months.