## Implicit Interest Rate

An implicit interest rate, sometimes referred to as an effective interest rate or imputed interest rate, is the rate of interest that is not explicitly stated in a contract or agreement but can be calculated from the terms of the agreement.

The implicit interest rate is often used in the context of leases or installment purchases, where it is the rate that makes the present value of all lease or installment payments equal to the original capital or principal amount.

For example, suppose you purchase a car under a lease agreement where you make a down payment and then monthly payments for a certain number of years. The implicit interest rate would be the rate that equates the present value of your down payment plus all your future lease payments to the initial cost of the car.

To compute the implicit interest rate, you may use various financial formulas or functions available in software such as Excel that solve for the interest rate given the present value, future value, number of periods, and payment amounts.

In the context of accounting, the implicit interest rate can be significant. For instance, under International Financial Reporting Standards (IFRS) and U.S. Generally Accepted Accounting Principles (GAAP), when accounting for leases, the lessee must determine the implicit interest rate in order to correctly classify and account for the lease. If the implicit rate can be readily determined, it should be used. If not, the company’s incremental borrowing rate may be used instead.

## Example of an Implicit Interest Rate

Let’s consider an example of a car lease agreement:

Suppose you lease a car that is worth $25,000 at the start of the lease. You make an immediate down payment of $5,000, followed by 36 monthly payments of $600.

The implicit interest rate in this lease is the rate that makes the present value of the down payment and all future lease payments equal to the initial cost of the car. In other words, it is the rate (r) that solves the following equation:

$5,000 + $600/(1+r) + $600/(1+r)^2 + … + $600/(1+r)^36 = $25,000

Solving this equation for r gives the monthly implicit interest rate, which can then be annualized by multiplying by 12 (assuming compound interest).

In reality, this calculation would typically be done using financial software or a financial calculator, as it involves solving for r in a somewhat complex equation. It is also worth noting that the calculation assumes that the $600 payments are made at the end of each month.

The implicit interest rate reflects the true cost of leasing the car. While the lease contract might not specify an interest rate, in effect, you are paying interest as part of your lease payments, and the implicit interest rate quantifies this cost.