Interest is a percentage of an initial amount, or "principal," added to that principal over a given period of time. In the case of a loan, that period of time will be the agreed length of time within which you will repay the loan. With an investment or savings deposit, it will be over the life of the investment or while there is money in the savings account. In this article, we examine and compare the simple and compound methods of calculating interest.
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What is simple interest?
Simple interest is a percentage of the principal added to that principal regularly. It can be expressed as a formula like this:
i = p x r
In other words, the interest (i) is the sum of the principal (p) multiplied by the interest rate (r). This gives you the amount of interest that will be added to the principal every accrual period—for example, every year. If you want to know how much interest will be added over the life of a loan, for example, you would multiply that interest by the time period:
i = p x r x t
In that formula, t is the duration of the loan.
How does simple interest work?
The way simple interest works can be demonstrated with these examples:
- Example 1: You take out a loan for $5,000 to be repaid over five years. The bank charges you a simple interest rate of 2.8 percent. Using the formula i = p x r x t, you can calculate the total amount of simple interest you will have to pay: 5,000 x .0.28 x 5, which comes to $700. You will pay a total of $700 in simple interest over 5 years.
- Example 2: You deposit $1,000 into a savings account that accrues 2.8% simple interest every month. The monthly interest amount is 1,000 x 0.028, which is $28. After 15 years, the total simple interest accrued will come to $5,040. That is, 1,000 x 0.028 x 180 (the number of months in 15 years).
What is compound interest?
Compound interest is a percentage of the principal amount including all previously-accrued interest. In other words, each interest-accruing period, the amount of interest added to the principal is calculated based on the principal plus the interest added in the previous period. To calculate the amount of compound interest you would accrue every year, you can use the following formula:
i = p x (1 + r)t - p
In that formula, p is the principal amount, r is the interest rate and t is the number of accrual or compounding periods in a year. If the number of compounding periods per year is more than one, you need to adjust the formula to this:
i = p x (1 + r/t)t x y - p
In this version of the formula, y is the number of years.
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How does compound interest work?
Compound interest is the most common form of interest you will see. It is used, for example, when you take out a line of credit. It is also used to calculate the interest your money accrues if you set up an interest-bearing account. To help you understand how it works, here is an example:
You set up a savings account with a deposit of $5,000. The bank applies a compound interest rate of 2.8 percent. Interest accrues every month.
After one month, your investment has added $11.67 in interest. You arrive at this by applying the formula: 5,000 x (1 + (0.028/12))1- 5,000. After two months, you have $23.36 in interest. This is the result of 5,000 x (1 + (0.028/12))2 - 5,000. After three months, the total interest is $35.08, or 5,000 x (1 + (0.028/12))3 - 5,000. By the end of the first year, you will have added $141.81 in compound interest.
At the end of five years, you will have added $750.43 in compound interest.
If the bank added compound interest to your deposit in annual installments, the numbers would come out differently. After the first year, you would have added $140 in compound interest to your deposit. After two years, this would become $283.92 in interest. By the end of the third year, your compound interest would be $431.86. At the end of the fifth year, you would have $740.31 added to your deposit in compound interest.
This demonstrates that compound interest applied to a savings account or an investment works out better for you the more frequently it accrues. For a loan payment, however, you would prefer less frequent accruals.
Simple vs. compound interest: differences
There are some significant differences between simple and compound interest:
- Simple interest is easier to calculate.
- Simple interest is always the same amount since it is a percentage of the principle. The compound interest amount will be different every accrual period since it is a percentage of the principal plus interest earned or accrued to date.
- The principal remains the same with simple interest. With compound interest, the compounded interest is added to the principal, increasing the principal amount.
- Since the interest charge and principal amount are the same every accrual period with a simple interest loan, you won't be charged for outstanding interest when you pay the loan off.
- Simple interest is better for purchases such as car loans since the cost of the loan is static. Compound interest is better for investing or saving since your funds will grow quicker.