# What is an implicit interest rate?

## Definition of Implicit Interest Rate

An implicit interest rate is one that is not stated explicitly.

## Example of Implicit Interest Rate

Assume that I lend you \$4,623 and you agree to repay me by giving me \$1,000 at the end of each year for 6 years. Obviously you are paying interest. However, our agreement did not specify any interest, nor did it state an interest rate. To find the interest rate that is implicit in this arrangement, you need to carry out what's known as a present value calculation. This can be done through the use of a financial calculator, software, an online calculator, or present value tables. The following format is helpful when using a present value of an ordinary annuity (PVOA) table:

• PVOA = PMT x PVOA factor for n=6, i=?
• \$4,623 = \$1,000 x PVOA factor for n=6, i=?
• \$4,623/\$1,000 = PVOA factor for n=6, i=?
• 4.623 = PVOA factor for n=6, i=?

The PVOA factor of 4.623 appears in the PVOA table in the row where n=6, and where i = 8%. Hence, this loan has an implicit interest rate of 8%.