Financial math: equivalent annual rate

Tutoring financial math, this is an important concept.  The tutor introduces it.

Back in my September 18 post, I discussed the general case of compound interest.

Now we turn to the question: how do we compare 3% interest compounded annually with 3% interest compounded monthly? Perhaps the first problem to notice is that both are called 3%.

While there might be a few definitions, the nominal rate, to many, means the number the interest is called, as opposed to what it truly is. Therefore, 3%, compounded monthly, is a nominal rate (from my point of view, anyway).

To find the equivalent annual rate, we can imagine one dollar is invested in the account for 12 months. Subtracting one dollar off the end amount leaves the interest. Since the interest is on one dollar, it’s also the interest rate.

We proceed:

A=1(1+0.03/12)^(12(1))=1.030415957

interest=A-P=1.03041597-1=0.030415957

The calculations above point to an annual interest rate of 3.0415957%.

So, a nominal rate of 3%, compounded monthly, is really an annual rate of 3.0415957%.

Financial calculators often have a function to find the equivalent annual rate from a nominal one. I’ll be discussing the calculator aspect in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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