What is the difference between the interest rate and the Annual Percentage Rate (APR)?
In the absence of APR affecting fees, one of our most common questions is “Why is the Actuarial APR (as defined in Appendix J to Regulation Z) different from the entered interest rate? Shouldn’t they be the same without fees?”
The answer is this: different accrual methods produce different payments, and the Actuarial Method1 is different from any other method used in the market2.
The lender’s accrual method computes a payment, P, with an interest rate, I.
If we change interest accrual method to the actuarial method, a different
payment, Pa, should be expected; however, if Pa is required to equal P,
the interest rate will have to be changed to achieve that objective. Call that
new interest rate, APR - the rate needed for the payments to be equal.
It’s for this reason the APR should be expected to be different from the entered interest rate. If, by chance, the lender’s accrual method produces the same payment as the Actuarial method, then the APR is equal to the lender’s interest rate; otherwise, the APR will be different from the entered interest rate.
Let’s take a closer look to understand why the APR is sometimes higher, sometimes lower than the entered interest rate.
Suppose the Actuarial payment, Pa, is less than the payment computed using the
lenders method of accrual. In that case, we would need to increase the interest
rate, APR, to match the payment. In other words, some APR > I would be
required in order for the two payments to be equal. This inequality is the
expression of an APR being greater than the entered interest rate.
Likewise, if the Actuarial payment is greater than the payment using the
lender’s method of accrual, APR must be decreased. This smaller interest rate
explains an APR being less than the lender’s interest rate.
In a sentence, the APR is the rate that produces the same payment using the actuarial method of interest accrual as the payment disclosed by the lender using the lender’s method of interest accrual.
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Technically, the Actuarial APR is not an interest rate, but rather a rate that balances the present values of advances with the present values of payments as described in Appendix J (b)(8). ↩
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Though the Actuarial Method is sometimes modeled as an interest accrual method to ensure the interest rate equals the APR, problems can occur. The Actuarial method compounds interest and some calendar configurations make it impossible for the entered rate to equal the APR. ↩