How to Calculate Interest Based on Number of Payments
Ongoing payments are frequently listed as a certain amount of money for a fixed term--for example, $100 a month for 24 months. Basic multiplication and division can be used to determine the interest rate being charged over that period of time. This is slightly more complicated with some contract terms, such as no interest due for six months, but can still be calculated on an annual basis. Terms should be compared with other loan arrangements to determine the value of the deal.
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Instructions
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Multiply the amount per payment by the total number of payments to determine the total cost of the contract. For example, $100 per month over 24 months results in a $2,400 total cost.
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Divide this by the amount you would pay for the item if you paid in full up front. If the same item above costs $2,000, then the interest paid out over the 24 month term is $2,400 / $2,000 = 1.2. 1.2 is equal to 120%, so you are paying 20 percent interest over the term of the contract.
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Divide this number by the number of years in the contract to determine the annual interest rate; the contract above is 20 percent over two years, so your interest rate is 10 percent per year. If the contract is less than a year, you would divide by a fraction. A 20 percent interest rate over a six-month contract, for example, is 20% / 0.5, or 40% per year.
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A similar calculation is used with more complicated payment terms. For example, take a purchase that requires no payments for the first six months, but which charges $225 a month for two years thereafter. The total cost of this contract is $125 * 24, or $3,000. That is 1.5 times the $2,000 cash purchase price, which is 50% over 30 months, or 2.5 years. This divides out to 20 percent per year interest.
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Tips & Warnings
The steps provide the simple interest rate; this determines the interest you pay on the initial cost, but assumes that no interest is paid on accrued interest. When you pay interest on past interest, as you do with credit cards, this is called compound interest. Calculating compound interest requires algebra; the formula for each payment is Cash Price * (1 + Interest)^Payments = Total. In the first example, $2,000 * (1 + Interest)^24 = $2,400. This solves to each monthly payment being 0.76% interest. Raise this to the power of the number of months in a year to calculate annual compound interest: 1.007^12 = 1.095, or 9.5 percent compound interest annually.
