Annual Percentage Rate
Some lenders charge lower interest but add high fees; others do the reverse. The Annual Percentage Rate (APR) allows you to compare loans on equal terms. It combines the fees with a year of interest charges to give you the true annual interest rate. All lenders are required under the Consumer Credit Protection Act to disclose the effective annual percentage rate as well as the total finance charge in dollars.
The APR is the true measure of the effective cost of credit. It is the ratio of the total finance charge, not just the interest charge, to the average amount of credit in use during the life of the loan and is expressed as a percentage rate per year. The calculation of the APR depends on whether the loan is repaid in a single payment or in installments.
Single-payment loans: The single payment loan is paid in full on a given date. There are two ways of calculating APR on single payment loans, the simple interest method and the discount method.
The simple interest method uses this formula:
APR = average annual finance charge/amount borrowed or proceeds
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Example
Suppose you borrow $1,000 at 10 percent for one year and there is a $25 application fee. The finance charge is $125, the interest plus the application fee.
Under the simple interest method, the total principal plus finance charge must be repaid at the end of the year.
APR = $125/$1,000 = 12.5%
Under the discount method, the finance charge is deducted from the amount of money loaned. So you get, and have the use of, only $875, the principal minus the finance charge.
APR = $125/$875 = 14.3%
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Installment loans. There are several methods for calculating the APR on installment loans:
- The actuarial method is the most accurate in calculating the APR and the one lenders most frequently use. It can be defined as interest computed on unpaid balances of principal at a fixed rate, with each payment applied first to interest and the remainder to principal. Since calculation by this method involves complicated formulas, the APR is commonly computed using annuity tables, software, or financial calculators.
- The constant-ratio method is used to approximate the APR on an installment loan by the use of a formula, but it overstates the rate substantially. The higher the quoted rate, the greater the inaccuracy.
- The direct-ratio method uses a somewhat more complex formula but is still easier than the actuarial method. It slightly understates the APR as compared to the actuarial method.
- The N-ratio method gives a more accurate approximation to the APR than either the constant-ratio or the direct-ratio method for most loans. The results of the N-ratio method may be either slightly higher or lower than the true rate, depending on the maturity of the loan and the stated rate itself.
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Example
Suppose you borrow $1,000 to be repaid in 12 equal monthly installments of $93. This represents a finance charge of $116.
[ ($93 x 12) - $1,000 = $116 ]
The APR calculated using each method is:
Actuarial Method: APR = 20.76%
Constant-ratio Method: APR = 21.42%
Direct-ratio Method: APR = 20.62%
N-ratio Method: APR = 20.76%
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As a loan is paid off it is said to be "amortized." The word amortize comes from French words meaning "to bring to death."
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