You have borrowed $130,000 to buy a new motor home. Your loan is to be repaid over 15 years at 8% compounded monthly. If you pay an extra $200 per month on the motor home, how many years will it take to pay off the loan?

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment for the original loan amount of $130,000 over 15 years at 8% compounded monthly. Using the formula:

P = (PV * r) / (1 - (1+r)^(-n))

where P is the monthly payment, PV is the present value (loan amount), r is the monthly interest rate (8%/12), and n is the total number of months (15*12).

We get:

P = (130000 * (8%/12)) / (1 - (1+(8%/12))^(-15*12)) 
P = $1243.96

This means that without any extra payments, it would take 15 years to pay off the motor home loan.

However, with an extra $200 per month, the new monthly payment becomes $1243.96 + $200 = $1443.96.

Using the same formula above, but using this new monthly payment, we can solve for the number of months it will take to pay off the loan:

P = (130000 * (8%/12)) / (1 - (1+(8%/12))^(-n)) + 200
$1443.96 = ($1083.33 / (1 - (1+(8%/12))^(-n))) + 200
$1260.63 = ($1083.33 / (1+(8%/12))^(-n))
(1+(8%/12))^(-n) = $1083.33 / $1260.63
(1+(8%/12))^n = $1260.63 / $1083.33
n = ln($1260.63 / $1083.33) / ln(1+(8%/12))
n = 138.28 months
n = 11.52 years

Therefore, it will take approximately 11.5 years to pay off the loan with the extra $200 payments.

You Have Borrowed $130,000 to Buy a New Motor Home