Nominal and Effective Interest Rates

Interest rates aren’t always as simple as they seem. The stated interest rate in a loan agreement is usually different than the economic cost that we effectively pay when we become the borrower.

It is important to understand the difference between nominal and effective interest rates.

A nominal interest rate is the interest rate that is stated by a lender. This rate has not been adjusted to include the effects of compounding. It is also called a simple interest rate.

An effective interest rate reflects the economic benefit that the lender is earning. The effective rate is always greater than the nominal rate due to the impact of compounding.

For example if a bank offered to lend me money at a nominal interest rate of 10%.

Let us assume the schedule of the amortization for the debt is quarterly.

The loan will absolutely cost you more than 10%. if you think about it, the bank isn’t really asking you to pay 10% once per year, it’s asking you to pay 2.5%, four times per year Whilst this is the same amount of cash over the course of a year you can’t ignore the timing difference because there is a time value of money.

To translate a nominal 10% interest rate into an annual effective rate, we need to first convert the annual, nominal interest rate into what’s known as a periodic interest rate, by simply dividing the nominal 10% by four compounding periods per year.

The periodic interest rate is 2.5%.

To then calculate the effective interest rate, we can use the formula

(1 + R) ⁿ- 1,

R is the periodic interest rate and n is the number of periods per year.

So, one plus the periodic interest rate, which is 10%, divided by four periods. So that’s 1.025, and we raise 1.025 to the fourth power, = 1.1038. then we subtract one, and we have an effective interest rate of 10.38%.

Excel makes it very easy to translate from a nominal rate to an effective rate by using a function called effect.

The effect function has only two arguments. We enter equals effect, and then we specify the nominal annual interest rate, and then we specify the number of compounding periods per year. We hit enter, and Excel confirms that a nominal 10% compounded four times per year equals 10.38%.

That equates to $3,800 of extra interest in the first year on a $1 million loan. Note however you are not actually paying $3,800 on that $1 million dollar loan, you still only paying $100,000 of interest on the $1 million dollar loan, but you are effectively giving the bank an extra $3800 because you’re paying four times per year, rather than once per year.

After the bank has your money, every quarter, they can lend it out to someone else and earn an extra $3800.

On the flip side, sometimes if you already know the annual effective interest rate, and you need to calculate the nominal rate.

Using excel you can use the nominal function which has only two arguments. We enter equals nominal, and then we specify the annual effective interest rate, and then we specify the number of compounding periods per year.

This calculation will confirm that an effective 10.38% is the equivalent to a nominal 10% compounded four times per year.

Now you will never be stuck if you need to convert a nominal interest rate to an effective interest rate, or the other way around.

I trust you find this post helpful. If you have any questions, feel free to contact me.