The annual interest rate on a credit card is 18% with interest compounded monthly. If a...

The annual interest rate on a credit card is 18% with interest compounded monthly. If a payment of $100 is made at the end of each month, how many months will it take to pay off an unpaid balance of $2,583.56 (assuming no additional purchases are made)?

Expert Solution

Future value of annuity for periodic payments at the end of each month is

where P=Periodic Payment, r=Rate of Interest and FV=Future Value

Given,

Unpaid amount is 2583.56 implies FV=2583.56

Rate of interest per annum is 18% implies r=0.18. For monthly compounding, r=(0.18/12)=0.015

Period Payment is 100 implies P=100

Therefore,

That is

Therefore,

Hence, it will take 22 months to pay off the unpaid balance

milcah answered 2 years ago

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