## 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%.