# How to calculate simple interest

## What is simple interest?

Simple interest is different than compounded, or compounding, interest. With compounding interest, you earn interest on your interest, so that your money grows exponentially.

But with simple interest, you don’t earn interest on your interest, you only earn interest on your principal balance. Therefore, your money grows linearly.

In this lesson we’ll look at simple interest and how it’s calculated. You’ll also be able to use it to figure out the total amount of money you have in an investment.

What is simple interest? Simple interest is the amount you earn on an investment each year. It’s called simple interest because you earn the same amount on the account every year (it doesn’t compound).

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## What is the formula for simple interest?

The formula for simple interest is

???I=Prt???

where

???I??? is the amount of interest earned in the account, in other words it’s the money earned from the interest rate over a certain time period.

???P??? is the principal (the original amount of money in the account).

???r??? is the interest rate as a decimal.

???t??? is the period of time.

Let’s look at an example of how simple interest is calculated.

## Interest earned on a single deposit

Example

If you deposit ???\$200??? into a savings account and it earns ???8\%??? in simple interest, how much interest will you earn on the account in ???4??? years? We know ???P=\$200???

???r=\frac{8}{100}=0.08???

???t=4??? years

If we plug these values into the formula for simple interest, we get

???I=Prt???

???I=(200)(0.08)(4)???

???I=\$64??? This means that in four years you’ll earn ???\$64??? in interest.

Let’s look at a different way to do the same problem in case you forget the formula.

First, we need to find the interest earned in one year, by multiplying the initial amount by the interest rate.

???\$200\cdot 8\%??? ???\$200\cdot0.08???

???\$16??? Because the account earns simple interest, that means the interest doesn’t compound, and the same interest is earned each year. We’re looking for the interest earned in four years so we multiply the interest earned in one year by ???4???. ???\$16\cdot4???

???\$64??? Simple interest is different than compounded, or compounding, interest. ## Another formula for calculating the amount in the account Let’s look at another formula. How is the amount in the account calculated? The total amount in the account is calculated by the formula ???A=P(1+rt)??? where ???A??? is the total amount in the account after a given time period ???P??? is the initial amount in the account (the principal) ???r??? is the interest rate as a decimal ???t??? is the time period Let’s do an example with this formula. Example If you deposit ???\$260??? into a savings account that earns ???5\%??? simple interest, how much is in the account after ???8??? years?

We don’t know ???A???, but we know

???P=\$260??? ???r=\frac{5}{100}=0.05??? ???t=8??? years If we plug these values into the formula, we get ???A=P(1+rt)??? ???A=\$260(1+0.05\cdot8)???

???A=\$364??? If you happen to forget this formula that’s okay too, you can think this through as well. First, we need to find the interest earned in one year, by multiplying the initial amount by the interest rate. ???\$260\cdot5\%???

???\$260\cdot0.05??? ???\$13???

Because the account earns simple interest, that means the interest doesn’t compound, and the same interest is earned each year. Since we’re looking for the account balance after eight years, we add the principal amount to eight years times the annual interest.

???\$260+8\cdot\$13???

???\$260+\$104???

???\$364??? Which means after ???8??? years you’ll have a total of ???\$364??? in the account.

Of course you could also use the formula ???I=Prt??? and then just add it to the original amount. That would work too.

Remember that sometimes you’ll need to round your answers and that’s okay, just round to the nearest cent!

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