Question

. Marco wants to buy a game system that costs $499. He has $250 in savings and earns $50 a month in allowance and tutoring. His parents offer to make him a user on their credit card, which has a 22.5% interest rate. If he uses a credit card to buy the game system and pays only the $50 he makes per month, without using any of his savings,, how much will he still owe after 6 months? ​

Answer 1

$243.42

Explanation:

You want to know the remaining balance if a $499 credit card charge is paid off at the rate of $50 per month for 6 months. The interest rate is 22.5%.

Future value

The future value of the account is given by ...

FV = P(1 +r/12)^n -p((1 +r/12)^n -1)/(r/12)

where P is the initial charge, p is the monthly payment r is the annual interest rate, and n is the number of months of payments.

In this case, we have ...

FV = 499(1 +0.225/12)^6 -50((1 +0.225/12)^6 -1)/(0.225/12) ≈ 243.42

Marco will still owe $243.42 after 6 months.

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Additional comment

After 10 months, he will have paid $500, and will still owe about $56.50.

We have assumed that a full month's interest is due with the first payment. Often, interest is only charged on the unpaid balance, so a balance paid in full on the first payment will have no interest charged. The answer to this question will depend on the specific credit card terms.

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