In this video we discuss what is interest earned on interest? We go through a detailed example, calculating interest earned on the principal or original investment and the interest earned on interest.
Transcript/notes
What is interest on interest? As an example, let’s say that you deposit $1000 into an investment that pays an annual interest rate of 12% and is compounded monthly.
Since we are given a yearly rate, but we need to calculate the interest amount per month, we need to convert the yearly rate to a monthly rate. To do this, we divide the yearly rate of 12% by the number of months in a year, 12. Which equals 1% per month.
So, the interest earned for month 1, will be $1000 times 1%, or .01, which equals $10. At this point, the $10 of interest earned is all from the principal amount of the $1000 original investment. And now the account has $1010 in it, the original $1000 plus the $10 of interest earned.
For the interest earned for the second month, it will be the new amount in the account, $1010, times the 1% monthly interest rate, which equals $10.10 of interest earned for month 2. So, for this $10.10 of interest earned, $10 is earned from the $1000 original investment, and $.10 is earned from the $10 of interest earned from month 1. So, this $.10 is interest earned on interest.
And now the account has $1020.10 in it.
For the interest earned for the third month, it will be the new amount in the account, $1020.10, times the 1% monthly interest rate, which equals $10.201 of interest earned for month 3. So, for this $10.201 of interest earned, $10 is earned from the $1000 original investment, and $.201 is earned from the $10 of interest earned from month 1 and the interest earned from month 2. So, this $.201 is interest earned on interest.
And now the account has $1030.301 in it.
After 3 months, there will be $30 of interest earned off the original $1000 investment, and $.301 of interest earned off of interest.
If no new money is deposited into the account by the investor, this account will continue in the same manner, making $10 a month of interest earned from the original $1000 investment and an increasing amount of interest earned on interest.
Here are the calculations for the first 12 months.
And here are the numbers after 10 years.
Chapters/Timestamps
0:00 Example set up
0:15 How to convert yearly interest rate to monthly interest rate
0:26 Amount of interest earned for 1st month
0:51 Amount of interest earned for 2nd month
1:24 Amount of interest earned for 3rd month
2:30 12 months of interest
2:47 10 years of interest
Chapters/Timestamps