Question

20. You owe $1,568.00 on a credit card with a limit of $2,200.00 at an interest rate of 11.3% APR. You pay $300.00/month until it is paid off. How many months does it take you to pay it off?

- 6 months
- 9 months
- 4 months
- 7 months

Answer 1

(a) 6 months

Explanation:

The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.

That formula is ...

A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.

__

Using the given information, we can solve for t:

300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))

1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))

(1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782

Taking logs, we get ...

-12t·log(1 +0.113/12) = log(0.950782)

t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years

This fraction of a year is ...

(12 months/year)(0.448739 years) = 5.38 months

It will take you 6 months to pay off the loan.