When you put money in a savings account, the bank pays you for using it. That payment is interest. With simple interest, each year you earn the same percent of the amount you put in.
Key idea
$$I = Prt$$ $I$ is the interest, $P$ the principal (the money you start with), $r$ the yearly rate as a decimal, and $t$ the time in years. The balance at the end is $P + I$.
Why it works
One year of interest is $r$ times the principal: $P \times r$. Simple interest pays that same amount every year, so after $t$ years you have $t$ of them: $(P \times r) \times t$. (Many real accounts pay "compound" interest, which also earns interest on old interest. You will meet that later.)
| Year | Interest that year | Balance at the end of the year |
|---|---|---|
| 0 | \$500 | |
| 1 | \$20 | \$520 |
| 2 | \$20 | \$540 |
| 3 | \$20 | \$560 |
Worked examples
Worked example: Interest and balance
You deposit \$800 at 3% simple interest per year. How much interest do you earn in 4 years, and what is the balance?
- $P = 800$, $r = 3\% = 0.03$, $t = 4$.
- $I = 800 \times 0.03 \times 4 = 96$.
- Balance: $800 + 96 = 896$.
Answer: \$96 of interest; balance \$896
Worked example: Time in months
\$1,200 earns 2.5% simple interest per year. How much interest after 6 months?
- Time must be in years: 6 months is $\frac{6}{12} = 0.5$ year.
- $I = 1200 \times 0.025 \times 0.5 = 15$.
Answer: \$15
Worked example: Finding the rate
A \$2,000 deposit earns \$150 of simple interest in 3 years. What is the rate?
- $150 = 2000 \times r \times 3$, so $150 = 6000r$.
- $r = 150 \div 6000 = 0.025$.
- As a percent, $r = 2.5\%$.
Answer: 2.5% per year
Common mistake
Two slips to watch: using $3$ instead of $0.03$ for 3% (the interest comes out 100 times too big), and using months as if they were years. Check: does the interest look like a small part of the principal?