Learn About Simple and Compound Interest
Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit as in the case of a certificate of deposit. Interest can be calculated in two ways, simple interest or compound interest.- Simple interest is calculated on the principal, or original, amount of a loan.
- Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."
There can be a big difference
in the amount of interest payable on a loan if interest is calculated
on a compound rather than simple basis. On the positive side, the magic
of compounding can work to your advantage when it comes to your
investments and can be a potent factor in wealth creation.
While simple interest and compound interest
are basic financial concepts, becoming thoroughly familiar with them
may help you make more informed decisions when taking out a loan
or investing.
Simple Interest Formula
The formula for calculating simple interest is:
Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.
Interest on this loan is payable at $500 annually, or $1,500 over the three-year loan term.
Compound Interest Formula
The formula for calculating compound interest in a year is:
Compound Interest = Total amount of Principal and Interest in future (or Future Value) less the Principal amount at present called Present Value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return.
Continuing with the simple interest example, what would be the amount of interest if it is charged on a compound basis ?
In this case, it would be:
$10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25.
While the total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into consideration accumulated interest of previous periods. Interest payable at the end of each year is shown in the table below.
| Year | Opening Balance (P) | Interest at 5% (I) | Closing Balance (P+I) |
| 1 | $10,000.00 | $500.00 | $10,500.00 |
| 2 | $10,500.00 | $525.00 | $11,025.00 |
| 3 | $11,025.00 | $551.25 | $11,576.25 |
| Total Interest | $1,576.25 |
Compounding Periods
When calculating compound interest, the number of compounding periods
makes a significant difference. Generally, the higher the number of
compounding periods, the greater the amount of compound interest. So for
every $100 of a loan over a certain period, the amount of interest accrued
at 10% annually will be lower than the interest accrued at 5%
semi-annually, which will, in turn, be lower than the interest accrued
at 2.5% quarterly.
In the formula for calculating compound interest, the variables "i" and "n" have to be adjusted if the number of compounding periods is more than once a year.
That is, within the parentheses, "i" or interest rate has to be divided by "n," the number of compounding periods per year. Outside of the parentheses, "n" has to be multiplied by "t," the total length of the investment.
Therefore, for a 10-year loan at 10%, where interest is compounded semi-annually (number of compounding periods = 2), i = 5% (i.e., 10% / 2) and n = 20 (i.e., 10 x 2).
To calculate total value with compound interest, you would use this equation:
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