Question

Paolo is paying off a credit card with a current balance of $450. The interest rate on the card is 23%. The minimum monthly payment is $25, but he plans to make monthly payments of $45. He will not be using the card to accumulate further debt. Approximately how many months will it take to pay off the balance?

Answer 1

This question requires application of PV of annuity, according to which

PV =

[1-(4+5)-) [1-(1+r)-n LT P= Periodic Payment r=rate per period n = number of periods

r = 23%/12 = 1.9167%

1-(1+0.019167)- 450 = 45 +一 0019167

10=- 1-(1+0.019167)- 0.019167

0.191967 = 1 - 1.019167^-n

1.019167^-n = 0.808333

Taking log of both sides,

-n * LN(1.019167) = LN(0.808333)

-n * 0.018985 = -0.21278

n = 11.21 months

Answer 2

The answer is 11