University of Nebraska–Lincoln Extension, Institute of Agriculture and Natural Resources
Know how. Know now.
Figuring the True Cost (APR) of Credit
Sandy D. Preston, Extension Educator Kathy Prochaska-Cue, Extension Family Economist
This publication will help you determine the exact annual percentage rate of a credit transaction.
The federal Truth in Lending law requires lenders to tell you the annual percentage rate (APR) and the total finance charge in dollars when you apply for credit. However, those figures still may not tell the whole story. In some cases, the exact annual percentage rate may not be known until all spe- cifics of the transaction have been decided.
When the creditor tells you the interest rate, you can be sure you are being quoted the true APR and that it is the rate being written into the credit contract by doing some simple calculations. These calculations also allow you to compare rates from different creditors for the best deal.
To do the calculation to find the true cost of borrowing, you would need to revise the formula, I = PRT to read R = I / PT. Then you could find the rate of interest by doing the following:
R = 30 / 250 = .12 = 12%
A $30 interest charge on an average outstanding balance of $250 is costing you 12 percent a year. In this case the true cost of borrowing or the approximate APR is twice as large as the stated interest rate.
The Effective Cost of Borrowing (APR)
Convert quoted interest rates to APR by using the fol- lowing formulas:
Use the simple interest rate formula
The finance charge is the amount of money you pay for the use of credit. When lenders state the finance charge, they must include the interest charge and any other fees that are part of the credit transaction. Examples of these other fees include a loan origination fee, any processing fees, premiums on credit life insurance, and any other fee that is a required part of the credit offer.
I = PRT
where I is the dollar amount of interest, P is the amount of principal borrowed, R is the rate of interest quoted, and T is time of the loan in years. When a lender quotes you a simple interest rate of 6 percent on a $500 loan borrowed for one year, the calculation would be:
I = $500 x 0.06 x 1 = $30
Use the following formula to determine the true effective cost of borrowing. It also will give the approximate annual percentage rate of interest (APR).
APR = 2 x f x n / a x (t+1)
where f is the amount of finance charge, n is the number of payments per year, a is the amount to be repaid, and t is the total number of payments.
But is that the true cost of borrowing?
Simple vs. Effective Interest Rates
Finding the True Effective Cost of Borrowing (APR)
In most instances you won’t be using the entire $500 for the entire year. Let’s assume the loan will be paid off in 12 equal monthly installment payments beginning in 30 days. You have full use of the entire $500 for only the first month. After the first month, the amount you have to use decreases throughout the year. The average monthly balance on the loan is approximately $250.
To illustrate the use of the effective interest rate formula or the APR, assume you agree to pay $440 for a washing machine. A down payment of $40 is made leaving $400 to be borrowed at a stated interest rate of 10 percent. The loan is to be paid off in 18 equal monthly installments.
The finance charge can be calculated using the simple interest rate formula, I = PRT:
I = $400 x 0.10 x 1.5 = $60