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 and compound interest are basic financial concepts, becoming thoroughly familiar with them will help you make better decisions when taking out a loan or making investments, which may save you thousands of dollars over the long term.
Basic Practical Examples
The formula for calculating simple interest is:
Simple Interest = Principal x Interest Rate x Term of the loan
= P x i x n
Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for a three-year period, 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.
The formula for calculating compound interest in a year is:
Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods for a year.
Continuing with the above 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.
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 interest accrued at 5% semi-annually, which will, in turn, be lower than 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” has to be divided by “n,” 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:
= [P (1 + i/n)nt] – P
= P [(1 + i/n)nt – 1]
where P = Principal, i = annual interest rate in percentage terms, n = number of compounding periods per year, and t = total number of years for the investment or loan.
The following table demonstrates the difference that the number of compounding periods can make over time for a $10,000 loan taken for a 10-year period.
|Compounding Frequency||No. of Compounding Periods||Values for i/n and nt||Total Interest|
|Annually||1||i/n = 10%, nt = 10||$15,937.42|
|Semi-annually||2||i/n = 5%, nt = 20||$16,532.98|
|Quarterly||4||i/n = 2.5%, nt = 40||$16,850.64|