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# Analysis of Credit Card Debt

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The amount of credit card debt is \$5,270.00 with an average APR of 15.53%. Considering the minimum monthly payment of \$120.00 determine the interest. How long will it take to pay off if only making minimum payments? If graphs or charts are available please include.

https://brainmass.com/math/consumer-mathematics/analysis-credit-card-debt-560123

## SOLUTION This solution is FREE courtesy of BrainMass!

This would be an annuity calculation.

Since you are using an APR (Annual percentage rate) of 15.53% (ia = 0.1553) it would mean that the monthly interest rate is 1.21% (im = 0.0121).

You can find this by finding the (1/12) root of (1+0.1553) which is the annual increase of your loan. i.e. (1.1553)1/12 = 1.0121.

Please note that sometimes in finance they just divide the Annual percentage rate by 12 in order to find the monthly rate i.e. 0.1553/12 = 0.0129. This is mathematically incorrect as a monthly interest of 0.0129 if compounded over 12 months (one year) would give an APR of 16.68%.

Now we know the monthly interest rate, we know the monthly repayment, we know the loan value and we need to find out the number of periods for full repayment. So we need to rearrange the formula above a little:

So there will be full repayment after 64 months (after 63 months there will be still some small repayment left). If you need to find how much the 64th repayment will be you can input the same values in the original annuity formula using 63 monthly repayments to find the remaining amount:

Of course this can be much better calculated (more accurately since more decimals are used) using excel (see attached excel worksheet).

So after 63 months (five years and three months) the loan will be almost repaid. So on the 64th month an amount less than 120 will be paid for full repayment.

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