How to Calculate Compound Interest on Unpaid Bills

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An unpaid bill from a creditor such as a credit card company typically accrues interest. A creditor generally charges compound interest, meaning that the interest itself also accrues interest. The compound interest on an unpaid bill depends on the initial amount of the bill, the payment period, the interest rate and the amount of time you allow the interest on the unpaid bill to accumulate. This procedure requires a scientific calculator with an exponent function.

Obtain the initial balance of the unpaid bill from the creditor. Assume for this example that the initial balance of the bill is $3,000.

Obtain the compounding period of the unpaid bill from the creditor. The compounding period is generally equal to the interval between expected payments. Assume for this example that the interest on the unpaid bill is compounded monthly.

Obtain the interest rate on the unpaid bill from the creditor. A credit card company typically provides the interest rates on an unpaid bill as an annual percentage rate, or APR. Assume the APR on the unpaid bill in this example is 12 percent.

Divide the unpaid bill's APR by 100 to get the unpaid bill's annual interest rate. The APR for the unpaid bill in this example is 12 percent, so the unpaid bill's annual interest rate is 12 / 100, or 0.12.

Divide the unpaid bill's annual interest rate by the number of compounding periods that the interest on the unpaid bill has in a year. This result provides the unpaid bill's interest rate for the compounding period. The unpaid bill's annual interest rate in this example is 0.12 and the compounding period is one month, so the interest rate on the unpaid bill over the compounding period is 0.12 / 12 = 0.01.

Determine the number of compounding periods you will allow the interest on the unpaid bill to accrue. Assume for this example that you plan to wait two years, or 24 compounding periods, before you pay the bill.

Calculate the balance for the unpaid bill with the formula B = P x (1 + I)^N. B is the final balance, P is the initial balance, I is the compounding period's interest rate and N is the number of compounding periods that you will allow the interest to accrue. The final balance for this example is B = P x (1 + I)^N = 3,000 x (1 + 0.01)^24 = $3,809.20.

Subtract the initial balance from the final balance to get the total compound interest on the unpaid bill. The final balance of the unpaid bill is $3,809.20 and the initial balance on the unpaid bill is $3,000, so the total compound interest on the unpaid bill in this example is $3,809.20 - $3,000 = $809.20.

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