Calculation of Interest
The two most common methods of calculating the interest portion of the finance charge use the simple interest and the compound interest formulas. You will end up paying more for the loan if the interest is calculated using compound interest. Also, the longer the longer the greater the different between what you will pay using compound interest and the difference you will pay using simple interest.
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Tip
Credit card interest is nearly always "compound" interest. However, because of the Truth in Lending laws, credit card companies must disclose the Annual Percentage Rate (APR) that they charge. So, for credit card companies, the math is done for you--you just have to wisely apply it to your situation.
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Simple interest. Simple interest is the dollar cost of borrowing money. This cost is based on three elements:
- the amount borrowed, which is called the principal (P);
- the rate of interest (R);
- and the time for which the principal is borrowed (t).
The formula used to find simple interest is: Interest (I) equals the principal (P) mulitpled by the rate of interest (R) multiplied by the amount of time the loan is outstanding (T). Expressed as a formula, this is: I = P x R x T
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Example
Suppose you borrow $1,000 at 10 percent simple annual interest and repay it in one lump sum at the end of 3 years. To find the amount that must be repaid, calculate the interest:
Interest = $1,000 x 0.10 x 3 = $300
This computes to $100 of interest each year. The amount that must be repaid is the $1,000 principal plus the $300 interest or a total of $1,300.
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Compound interest: Unlike simple interest, compound interest calculates interest not only on the principal, but also on the prior period's interest. The formula for calculating compound interest is: the future repayment value (F) equals the principal (P) multiplied by (1 + rate of interest(R)) raised to the power of amount of time (T).
This can be expressed by the following mathematical formula: F = P x (1 + R)T
The factor (1+ R)T can be obtained easily using pencil and paper, a calculator, or a compound interest table. Most consumer loans use monthly, or even daily compounding. Thus, if you are dealing with monthly compounding, the "R" term in the above formula relates to the monthly interest rate, and "T" equals the number of months in the loan term. Likewise, if the loan in question uses daily compounding, the "R" term relates to the daily interest rate, and "T" equals the number of days in the loan term.
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Example
Suppose you borrow $1,000 at 10 percent interest, compounded monthly, and repay it in one lump sum at the end of three years. To find the amount that must be repaid, you must first convert the 10 percent annual interest rate into a monthly interest rate:
0.10 (or 10%) / 12 = 0.00833
Plugging this number into the formula yields:
- F = $1,000 x (1 + .00833)36
- F = $1,000 x (1.00833)36
- F = $1,000 x (1.34802)
- F = $1,348.02
Thus, you pay $348.02 of interest on the original loan. This is nearly $50 more than you would have paid if the lender charged simple interest.
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