Question

Your credit card charges an APR of 29% on your balance. Interest is compounded on a daily basis, 365 days a year. If you made the minimum payment of $150 per month on your credit card balance, how long will it take you to pay off a $5,000 balance?
Multiple Choice
6.61 years
35.73 years
2.98 years
5.82 years
9.56 yearsYour credit card charges an APR of 29% on your balance. Interest is compounded on a daily basis, 365 days a year. If you made the minimum payment of $150 per month on your credit card balance, how long will it take you to pay off a $5,000 balance? Multiple Choice 6.61 years 35.73 years 2.98 years 5.82 years 9.56 years

Answer 1

Given about a credit card due,

Amount due PV = $5000

Monthly payment PMT = $150

Interest rate = 29% per year compounded daily.

First we need to calculated monthly rate. And for monthly rate we first need effective annual rate.

Effective annual rate is calculated using formula

EAR = (1+APR/n)^n - 1

for daily compounding, n = 365

So, EAR = (1+29/365)^365 - 1 = 33.63%

Monthly compounded rate r is calculated using formula

Monthly compounded rate r = n*(((1+EAR)^(1/n)) - 1) = 12*(((1+0.3363)^(1/12)) - 1) = 29.34%

Let it take t years to payoff the balance. It can be calculated using PV formula of annuity.

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

5000 = 150*(1 - (1+0.2934/12)^(12*t))/(0.2934/12)

=> 0.815 = 1 - 1.0245^(12*t)

=> 1.0245^(12*t) = 1.815

=> 12*t = LN(1.815)/LN(1.0245)

=> t = 5.82 years

So it will take 5.82 years to pay off the balance.

Option d is correct.