How Do I Figure the Interest Rate on a Loan?

Most loans are advertised with a set interest rate, which can be fixed or variable over the lifetime of a loan. However, some loans are structured such that a fixed dollar amount is loaned at the beginning of the loan period, and another fixed dollar amount is due to service the loan at the end of that period. These loans can be compared with interest-based structures by calculating the interest rate that results in the amount due.

1. Divide the amount of the additional payment by the amount loaned to determine the simple interest rate. For example, consider a loan of $1,000, which must be repaid in one year with the amount of $1,300. This is $300/$1,000, or 30 percent per year, which is a hefty interest rate. However, if the loan was $10,000, and required a repayment of $10,300, that is an interest rate of $300/$10,000, or 3 percent per year, which is extremely low.

2. Calculate the compound interest rate, in which you are paying interest on both the amount of the loan and the interest accrued, by using exponentials. As the interest rate is charged against the total balance each period, the formula is (1 + Interest Rate)^Periods. For example, we have determined that $300 on a $1,000 loan is 30 percent in simple interest. To compare this with a credit card, we must determine the compound interest rate. First, determine the number of compounding periods over the lifetime of the loan; in the example, this is 365 (days in a year). This yields the following algebraic formula, where X is the daily interest rate: 1,000 * (1 + X)^365 = 1,300 (1 + X)^365 = 1.3 (1 + X) = 1.000719 X = .000719 This can be compared with the daily interest rate on a credit card statement, or multiplied by 365 to compare it to the credit card's Annual Percentage Rate (APR). This shows that the APR of this loan is 26.2 percent, but after compounding, it results in total paid interest of 30 percent.

3. Determine the cost of a short-term loan by expanding it over the course of a year. For example, a payday loan store may charge $50 for a $1,000 loan, due in two weeks' time. This is a rate of 5 percent for the two weeks, but once those two weeks are multiplied by 26 (the number of two-week periods in a year), the simple interest is shown to be 130 percent–a very expensive loan. If additional fees and interest are levied after the initial two week period, this interest rate can skyrocket even higher.

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