Math Core

When you put money in a savings account, the bank pays you extra for letting it use your money. When you borrow money, you pay extra for the privilege. That extra money is called interest, and it's set by a percent.

Words you need

Definition

Simple interest

The principal is the amount of money you start with (deposit or borrow). The interest rate is the percent of the principal paid as interest each year. Simple interest is interest paid only on the principal, the same amount every year.

Suppose you deposit $500 in an account that pays $4\%$ simple interest per year.

Each year you earn $0.04 \times 500 = 20$ dollars.
After 1 year you've earned $20, after 2 years $40, after 3 years $60.

The interest grows by the same $20 every year, so the interest earned is proportional to the number of years.

Years	0	1	2	3	4
Interest earned ($)	0	20	40	60	80
Balance ($)	500	520	540	560	580

The formula

Multiply one year of interest by the number of years, and you get a formula.

Simple interest formula

I = P \cdot r \cdot t

$I$ = interest (in dollars)
$P$ = principal (in dollars)
$r$ = yearly interest rate, written as a decimal
$t$ = time in years

The total amount after $t$ years is the principal plus the interest: $A = P + I$ .

Worked example: Interest earned

Keisha deposits $1,200 in an account that pays $3.5\%$ simple interest per year. How much interest does she earn in 4 years? What is her balance then?

I = 1{,}200 \times 0.035 \times 4 = 168

She earns $168 in interest. Her balance is $1{,}200 + 168 = 1{,}368$ dollars, or $1,368.

Worked example: Borrowing money

Omar borrows $3,000 to buy a used car. The loan charges $6\%$ simple interest per year for 3 years. What is the total he must pay back?

I = 3{,}000 \times 0.06 \times 3 = 540

He pays back $3{,}000 + 540 = 3{,}540$ dollars, or $3,540.

Time that isn't whole years

The rate is a yearly rate, so time must be in years. Change months to years by dividing by 12.

Worked example: Time in months

Find the simple interest on $800 at $5\%$ per year for 18 months.

18 months is $\dfrac{18}{12} = 1.5$ years.

I = 800 \times 0.05 \times 1.5 = 60

The interest is $60.

Common mistake

Two mix-ups cause most wrong answers. First, write the rate as a decimal: $5\%$ is $0.05$ , not 5. Second, write the time in years: 18 months is $1.5$ , not 18. Using $t = 18$ would give $720 in interest, twelve times too much.

Finding the rate, principal or time

If you know three of the four values in $I = Prt$ , you can find the fourth. Substitute what you know, multiply the known numbers together, then divide.

Worked example: Find the rate

Lena earned $90 in simple interest on $1,500 over 2 years. What was the yearly interest rate?

\begin{aligned} 90 &= 1{,}500 \times r \times 2 \\ 90 &= 3{,}000r \\ r &= \frac{90}{3{,}000} = 0.03 \end{aligned}

The rate is $0.03$ , or 3% per year.

Tip

Check whether you're asked for the interest or the total amount. "How much interest" means $I$ . "How much will be in the account" or "how much is paid back" means $P + I$ .