Calculating Simple Interest

What is interest?

Interest is a percentage rate that is paid on borrowed money.

Sometimes, that interest is paid by a person to a lender or bank (when that person borrows money).

Other times, that interest is paid to a person by a lender or bank (when that person deposits money that the bank can then lend to other people).

When someone borrows or deposits money, they are given an interest rate (usually in percentage form).

The amount that they borrow or deposit is called the principal.

To calculate the interest that that person earns or has to pay, you just multiply the principal by the interest rate.  You perform this multiplication problem in the same way you would find the percent of any other number (see our Percent: Finding percent of a number Lesson for more).

To calculate interest, you can use a proportion (as in the Percent: Finding percent of a number).  You may also just choose to multiply (especially if it's a straightforward interest calculating question. 

Let's try a simple interest problem:

Example: You borrow \$500 from a bank. The interest rate is 7%.  How much will you pay in interest for the year?

To calculate simple interest, you multiply the principal (\$500) times the interest rate (7%).  Remember, you'll need to turn the percent into a decimal in order to do the multiplication:

$$\eqalign{\text{Principal}\times \text{Interest Rate} &= \text{Interest Due}\\500 \times .07 &= 35\\\text{You owe \$35 in interest}}$$ 

Notice that that question specifically asked about the amount of interest you'd pay for the year.  That's because most interest is annual.  If you borrow for many years, you will probably have to pay more interest (the amount of interest, annually).  

So, the complete formula for simple interest is:

$\large{\text{Simple Interest}= \text{Principal} \times \text{Interest rate} \times \text{Number of years}}$

Let's try an example with multiple years.

Example:You deposit $700 in the bank.  The interest rate is 3% per year.  How much interest will you earn in 6 years?

$$\eqalign{\text{Principal}\times \text{Interest Rate} \times \text{Number of years} &= \text{Interest Earned}\\700 \times .03 \times 6 &= 126\\\text{You earn \$126 in interest in six years}}$$ 

This formula also works when you do not borrow money for a full year.

Example: You borrow $20,000 to pay for college.  The interest rate is 5% per year.  After 6 months, you realize that you don't need the money because you earn enough at your part-time job to pay your tuition.  You pay the money back.  How much interest do you have to pay?

How many years will you be keeping the loan?  6 months equals $\dfrac{1}{2}$ of a year.  So, use $\dfrac{1}{2}$ or $.5$ as your number of years.

$$\eqalign{\text{Principal}\times \text{Interest Rate} \times \text{Number of years} &= \text{Interest Paid}\\20,000 \times .05 \times .5 &= 500\\\text{You pay \$500 in interest after 6 months}}$$ 

Remember, not all interest is simple interest.  Some interest is compound interest, and compound interest grows much faster than simple interest. It has a formula that involves exponents!  See Percents: Calculating Compound Interest to learn more.