Simple vs. Compound Interest: Definitions, Formulas and Examples

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.

There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound basis rather than on a 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.

The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

Simple vs. Compound Interest

What is compound interest?

Compound interest is a percentage of the principal amount including all previously accrued interest. In other words, for 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. As a borrower, compound interest can work against you as interest accrues faster than you can pay down the principal.

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:

I = p x (1 + r/t)t x y – p

In this version of the formula, y is the number of years.

Compound interest examples

The way simple interest works can be demonstrated with these examples:

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.

What is simple interest?

I = p x r

The interest (I) is the sum of the principal (p) multiplied by the interest rate (r) and is the amount to 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, 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.

Simple interest examples

The way simple interest works can be demonstrated with these examples:

You borrow $5,000 to be repaid over five years. The bank charges you a simple interest rate of 2.8%. It’s a fixed percentage that won’t change. Using the formula I = p x r x t formula to calculate the total amount of simple interest you owe: 5,000 x .0.28 x 5, which comes to $700. You will pay a total of $700 in simple interest over five years.

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 be $5,040. That is, 1,000 x 0.028 x 180 (the number of months in 15 years).

Simple vs. compound interest differences

There are some significant differences between simple and compound interest:

FAQ

What is better simple interest or compound interest?

When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate. Compound interest comes into play when you’re calculating the annual percentage yield. That’s the annual rate of return or the annual cost of borrowing money.

What is the difference between simple interest and compound interest with examples?

Learn more about Simple and Compound Interest in more detail here. If the difference between compound and simple interest is of three years than, Difference = 3 x P(R)²/(100)² + P (R/100)³.

How do you tell the difference between simple and compound interest?

Learn more about Simple and Compound Interest in more detail here. If the difference between compound and simple interest is of three years than, Difference = 3 x P(R)²/(100)² + P (R/100)³.

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