Question

You have just entered an MBA program and have decided to pay for your living expenses using a credit card that has no minimum monthly payment. You intend to charge $1, 000 per month on the card for the next 21 months. The card carries a monthly interest rate of 1%. How much money will you owe on the card 22 months from now, when you receive your first statement postgraduation?

Answer 1

Given

Monthly interest rate= 1%

Charges = $ 1000 per month

Since we are not paying monthly installments let us compute the future value of the amount required to be payable at the end of 21 Months

We know that

Future Value of Annuity = C[{( 1+i)^n -1}/i]

Here C = Cash flow per period

I = interest rate

n = Number of payments

Future Value = $ 1000[ { ( 1+0.01)^21 -1 } /0.01]

= $ 1000[ { { 1.01)^21 - 1} /0.01]

= $ 1000[ {1.232392-1}/0.01]

= $ 1000[ 0.232392/0.01]

= $ 1000[ 23.23919]

= $ 23239.19

Since in the question it is stated the amount due in 22nd month therefore we are required to calculate interest for one more month

Amount that is required to be payable in 22nd month= Future value of the amount in 21nd month ( 1+interest rate)

= $ 23239.19( 1+0.01)

= $ 23239.19*1.01

= $ 23471.58

The amount we owe on Credit Card is $ 23471.58 at the end of 22nd month.

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