Simple interest is a way to calculate how much money you earn (or owe) on an investment or loan over time. It depends on three things: how much money you start with, the interest rate, and how long the money sits. This formula shows up constantly in real-world finance, so it's worth getting comfortable with it now.

Simple Interest Formula

The core formula is:

$I = Prt$

Here's what each variable means:

$I$ = interest earned (or owed)
$P$ = principal, the initial amount invested or borrowed
$r$ = annual interest rate written as a decimal (so 5% becomes 0.05)
$t$ = time in years

Finding interest: Multiply all three values together. If you invest $1,000 at 5\\% for 3 years: $$I = 1{,}000 \times 0.05 \times 3 = 150$$. You'd earn$ 150 in interest.

The formula can also be rearranged to solve for any variable you're missing:

Find the principal: $P = \frac{I}{rt}$ $P = \frac{I}{r t}$
- If you earned $150 at 5% over 3 years: $P = \frac{150}{0.05 \times 3} = 1{,}000$
Find the rate: $r = \frac{I}{Pt}$ $r = \frac{I}{Pt}$
- If $1,000 earned $150 over 3 years: $r = \frac{150}{1{,}000 \times 3} = 0.05$ , which is 5%
Find the time: $t = \frac{I}{Pr}$ $t = \frac{I}{P r}$
- If $1,000 earned $150 at 5%: $t = \frac{150}{1{,}000 \times 0.05} = 3$ years

The trick is always the same: isolate the variable you need by dividing the interest by the product of the other two.

Simple interest formula calculations, Math. Sc. UiTM Kedah: Simple Interest

Real-World Financial Applications

Simple interest shows up in savings accounts, certificates of deposit (CDs), and many short-term loans.

For a savings account, the principal is your initial deposit, the rate is the annual percentage yield (APY), and the time is how long you leave the money in.
For a loan, the principal is the amount you borrow, the rate is the annual percentage rate (APR), and the time is how long you take to repay it.

Example: You borrow $5,000 at 6\\% APR for 2 years. The interest you owe is $$I = 5{,}000 \times 0.06 \times 2 = 600$$. So you'd pay back the original$ 5,000 plus $600 in interest, for a total of $5,600.

Time Unit Conversions

The rate in the formula is annual, so the time must also be in years. If you're given months or days, you need to convert.

Months to years: Divide by 12. For example, 6 months = $\frac{6}{12} = 0.5$ years.
Days to years: Divide by 365. For example, 90 days = $\frac{90}{365} \approx 0.247$ years. (Some banks use 360 days instead of 365, so check the problem.)

Example: You deposit $2,000 at 4\\% simple interest for 9 months. First convert: $$t = \frac{9}{12} = 0.75$$ years. Then calculate: $$I = 2{,}000 \times 0.04 \times 0.75 = 60$$. You'd earn$ 60 in interest.

Beyond Simple Interest (Preview)

As you move forward in math and finance, you'll encounter more complex ideas built on top of simple interest:

Compound interest calculates interest on both the original principal and any interest already earned. This makes money grow faster over time.
Future value is the total amount an investment will be worth at a later date.
Present value is what a future sum of money is worth right now.
Amortization is how loans get broken into equal payments over time (like a car payment or mortgage).

You don't need to calculate these yet, but recognizing the terms is helpful. For now, focus on mastering the simple interest formula and its rearrangements.