Calculating Compound Interest
The term “compound interest” denotes the fact that we do not actually pay the interest at the end of the year (or at a different set time as regards the interest payment). The interest is added to the principal, and from that point in time, the interest is calculated on the updated principal.
This can also be described as follows: at the end of the year, we return the principal, as well as the interest, and immediately receive another loan equal to the amount that we have paid off (including principal + interest).
Whenever compound interest is involved, we always specify a specific rate of nominal interest and together these are used as a basis for calculating the compound interest.
Example:
Bill received a $10,000 three-year loan at 8% nominal interest. Both the principal and interest will be paid at the end of the period. What sum of money will Bill repay at the end of three years?
The solution is $12,597. The stages of the calculation are shown in the following table:
| Principal amount updated at start of year | Interest amount for year | Principal amount updated at end of year | |
| Year 1 | $10,000 | $10,000 * 8% = $800 | $800 + $10,000 = $10,800 |
| Year 2 | $10,800 | $10,800 * 8% = $864 | $864 + $10800 = $11,664 |
| Year 3 | $11,664 | $11,664 * 8% = $933 | $933 + $11,664 = $12,597 |
Adjusted Interest
Adjusted interest is one of the “tricky” calculation methods developed by lenders.
Adjusted interest is based upon a specific rate of nominal interest. For example, we can calculate a 12% nominal interest rate by using one of the “tricks”, which we will explain by giving an example.
John received a $10,000 loan at 12% nominal interest, to which the following conditions are attached:
At the end of every three months (the fiscal quarter), the amount of interest will be calculated for that period.
The interest for a quarter is 3% (12% x 1/4).
The amount of interest after the first quarter is $300 (3% of $10,000).
The amount of interest per quarter is not actually paid. It is added to the principal at that time. The principal is now updated to $10,300.
In the second quarter, the amount of interest for the quarter is calculated again, and it is now $309 (3% of 10,300). The sum of $309 is added to the principal at the end of the second quarter, and the updated principal is now $10,609. At the end of every quarter, the amount of interest accumulated during that quarter is added to the sum of the principal.
The value of the principal is calculated as follows:
| Before Q1 | During Q1 | After Q1 | During Q2 | After Q2 | During Q3 | After Q3 | During Q4 | After Q4 |
| $10,000 | $300 interest | $10,300 | $309 interest | $10,609 | $318 interest | $10,927 | $328 interest | $11,255 |
It is evident that adjusted interest is calculated according to the same format as compound interest. Instead of once a year, however, it is calculated for shorter periods. In our example, adjusted interest is calculated as compound interest on a quarterly basis. Had we calculated the amount of interest every month, we would have stated that the adjusted interest was calculated on a monthly basis.
In our example, the amount of interest is $1,255, and the percentage of adjusted interest is 12.55% (=1,255/10,000).
The adjusted interest denotes the interest that we must actually pay for the loan.
If, for example, we have received a one-year loan, and the bank indicates that the adjusted interest for the loan (calculated on a quarterly basis) is 13%, then this means that we must pay back $11,300 ($10,000 in principal and $1,300 in interest).
DIY Spreadsheet
Click below to download a spreadsheet that would help you calculate compund interest yourself.
[gfs_button url=”http://gfs-upload-media.s3.amazonaws.com/DIY_Finance/spreadsheets/DIY_Compund_Interest.xlsx” target=”_self” existing_buttons=”gfs-main-download-button”]Download Spreadsheet[/gfs_button]
Test Yourself!
If you want to start investing on your own and start building your own portfolio you will need to learn the basics or at least get to know the options that are available to you. You can do that by reading the Introduction To Investing which will give you an insight into the different ways you can invest your money.
