Implicit interest rate – definition and example

An implicit interest rate refers to a loan in which there is no mention of an interest rate. However, there is interest on the loan because the borrower pays back more than he or she borrowed. Even so, the arrangement or contract makes no mention of any interest rate. Therefore, the rate is ‘implicit.’

If something is ‘implicit’ it means that we have suggested it but not directly expressed it. In other words, we ‘implied‘ it.

These types of loans are common among friends, family, and other informal situations. We also see them in lease agreements.

Banks and other financial institutions, on the other hand, tend to have contracts which mention interest rates.

The term ‘implicit interest rate’ simply means that nobody has explicitly mentioned an interest rate. There is no mention of it either verbally or in writing.

In the world of leases, people often use the word ‘implied‘ with the same meaning as ‘implicit.’

Pocket Sense has the following definition of the term:

“An implicit interest rate is a rate which is not explicitly stated. For example, a client may offer to pay in multiple installments instead of up-front, but not have the sophistication, or need, to explicate the interest rate implied by the offer.”

Implicit Interest Rate - mathematical calculation
An agreement with an implicit interest rate does not mention an interest rate. However, one exists, i.e., the agreement implies there is one. As you can see in this image, there is a simple mathematical formula to work it out.

Explicit vs. implicit interest rate

An implicit interest rate contrasts with an explicit interest rate. Explicit interest rates are those that appear clearly in any loan contract or agreement.

If I borrow, for example, $1,000 from my bank, I will have to pay back the principal plus interest. The principal is the original $1,000.

The loan contract will state whether there is a fixed or variable interest rate on the loan. In other words, it is an explicit interest rate.

The interest rate tells us how much interest the borrower must pay over a one-year period. The ‘interest‘ is the additional money the borrower pays back on top of the principal.

Calculating the implicit interest rate

Let’s suppose John borrows $10,000 from his sister, Mary. He agrees to pay it back within 12 months plus an additional $2,500. The additional $2,500 is interest.

In this arrangement, they have not mentioned any interest rate, i.e., it is an implicit interest rate.

How can we determine what the implicit interest rate is in John and Mary’s agreement? We need to do a mathematical calculation.

We divide the additional money by the principal and then multiply by 100. See below:

(Interest ÷ Principal) x 100 = Interest Rate
($2,500 ÷ $10,000) x 100 = 25%.

This is a very simple situation because John pays his sister back in twelve months. We typically calculate interest rates for a twelve-month period.

The implicit interest rate would be different if he paid her back over a longer period. It would also be different if John paid back in irregular installments.

Double-Entry-Bookkeeping.com says the following regarding implicit interest rates:

“Generally, the implicit interest rate can be shown to be the internal rate of return (IRR) of all the cash flows associated with a loan agreement.”