Question

You have a $20,000 balance on your credit card, which has an interest rate of 21% compounded quarterly. How many years will it take you to pay off the balance by making monthly payments of $800?

show alll work of have to isolate t

Answer 1

Rate of interest = Quoted rate = R= 21% compounded quarterly

No of compounding periods in a year = no of quarters in a year = n = 4

Effective annual interest rate = [1 + (R/n)]ⁿ - 1 = [1+(21%/4)]⁴ - 1 = [ 1 + 5.25%]⁴ - 1 = [ 1.0525]⁴ - 1 = 1.22712390 - 1 = 0.22712390 = 22.712390%

Monthly rate = [1+Effective annual rate]^1/12 - 1 = [1 + 22.712390%]^1/12 - 1 = [1.22712390]^1/12 - 1 = 1.017202 - 1 = 0.017202 = 1.7202%

Initial balance of credit card = Loan = $20000, Monthly payments = $800

We can find the number months it takes to pay of the credit card balance using NPER Function in excel

Formula to be used in excel: =NPER(rate,-pmt,pv)

Using NPER function in excel, we get number of months to payoff the balance = 32.9629 months

No of years to payoff the balance = No of months to payoff the balance / 12 = 32.9629 / 12 = 2.7469 years

Hence No of years to payoff the balance = 2.7469 years