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Simple Interest

When you put money in a savings account, the bank pays you a little extra for leaving it there. When you borrow money, the lender charges you a little extra for the loan. That extra money is called interest, and simple interest is the most basic way to calculate it.

Simple interest uses one formula: I=prtI = prt. Every simple interest problem — earning it or owing it — is the same three-number multiplication. The only place students slip is forgetting to write the percent as a decimal first.

The formula: I = prt

In I=prtI = prt, the letter pp is the principal — the starting amount you deposit or borrow. The letter rr is the interest rate, written as a decimal. The letter tt is the time in years. Multiply all three and you get II, the interest.

That is the whole formula. A deposit of $500 at 4% for 3 years earns I=5000.043=60I = 500 \cdot 0.04 \cdot 3 = 60, so $60 of interest. The interest is the same amount every year — 3 years just means three equal payments of it.

Write the rate as a decimal

The rate in the problem is a percent, but the rate in the formula must be a decimal. Move the decimal point two places left: 4%=0.044\% = 0.04, 5%=0.055\% = 0.05, 12%=0.1212\% = 0.12.

If your answer looks a hundred times too big — like $9,000 of interest on a $600 deposit — you almost certainly multiplied by the percent number instead of the decimal. That one habit catches most simple interest mistakes before they happen.

Interest vs. the total

Read the question carefully: some problems ask for the interest, and some ask for the total. The interest is just I=prtI = prt. The total is the principal plus the interest: total=p+I\text{total} = p + I.

This works in both directions. A saver's total is the balance in the account; a borrower's total is the amount paid back. Either way, find II first, then add the starting amount.

Worked examples

Example 1: interest earned on a deposit

You deposit $500 at 4% simple interest for 3 years. How much interest do you earn?

Start with the formulaI=prtI = prt
Write the rate as a decimal4%=0.044\% = 0.04
Substitute the principal, rate, and timeI=5000.043I = 500 \cdot 0.04 \cdot 3
MultiplyI=60I = 60

Answer: $60 of interest

Example 2: total paid back on a loan

You borrow $1,200 at 5% simple interest for 2 years. How much do you pay back in all?

Find the interest firstI=12000.052I = 1200 \cdot 0.05 \cdot 2
MultiplyI=120I = 120
Add the principal to the interest1200+120=13201200 + 120 = 1320

Answer: $1,320 paid back in all

Example 3: a longer time

You deposit $800 at 3% simple interest for 4 years. How much interest do you earn?

Write the rate as a decimal3%=0.033\% = 0.03
Substitute into the formulaI=8000.034I = 800 \cdot 0.03 \cdot 4
MultiplyI=96I = 96

Answer: $96 of interest

Try one yourself

Common questions

What do the letters in I = prt stand for?

pp is the principal (the starting amount), rr is the rate written as a decimal, and tt is the time in years. Multiplying them gives II, the interest.

Do I multiply by the percent or the decimal?

Always the decimal. Move the decimal point two places left first: 5%=0.055\% = 0.05. If you multiply by 55 instead, your answer comes out a hundred times too big.

What if the time is given in months?

Convert to years before you substitute, because tt counts years. Six months is t=0.5t = 0.5, and 18 months is t=1.5t = 1.5.

What is the difference between the interest and the total?

The interest is only the extra money, I=prtI = prt. The total — the balance in a savings account, or the amount a borrower pays back — is the principal plus the interest.

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