In this video we discuss how to convert the nominal interest rate to the effective interest rate. We go through the formula for the conversion and an example of the conversion
Transcript/notes
The nominal interest rate is the stated rate and it does not take into account different compounding periods. The effective rate of interest does take into account different compounding periods.
As an example, if a bank pays a stated nominal annual interest rate of 7.5%, that compounds quarterly, so 4 times per year, and someone invests $10,000 into this account, what is the effective annual interest rate?
The formula to calculate the effective interest rate is effective annual interest rate equals, the quantity 1 plus the nominal annual interest rate divided by the number of compounding periods, raised to the number of compounding periods minus 1. And here is a shortened version of the formula with all of the variables listed.
Using our formula, we have effective rate equals, 1 plus, 0.75, the decimal value of 7.5%, divided by 4, raised to the 4, minus 1. Here is this calculated out, which equals, 0.077136, or 7.71% rounded off as the effective rate, or real rate of interest.
So, using this rate of 7.71%, if we multiply the $10,000 times it, we get $771.36, and this is the amount of interest someone would make in 1 year.
Chapters/Timestamps
0:00 What is the nominal and effective interest rates
0:10 Example set up
0:24 Formula to convert the nominal rate to the effective rate
0:43 Example how to convert nominal rate to the effective rate
1:06 Calculate interest earned using the effective rate