Simple Interest

When you borrow money or invest it, there is a cost or reward: interest. Simple interest is the most straightforward way to calculate that amount. Understanding it is a crucial step in financial literacy.

The Formula

I = P \times R \times T

Variable	Meaning	Example
I	Interest earned or owed	$150
P	Principal (starting amount)	$1,000
R	Rate (annual, as a decimal)	5% = 0.05
T	Time (in years)	3 years

The total amount after interest is: A = P + I.

Worked Example 1: Savings Account

You deposit $2,000 in an account earning 4% simple interest per year. How much interest do you earn in 5 years? What is the total balance?

Identify: P = $2,000, R = 0.04, T = 5
Calculate interest: I = 2,000 × 0.04 × 5 = $400
Total: A = $2,000 + $400 = $2,400

Worked Example 2: Loan

You borrow $5,000 at 8% simple interest for 3 years. How much do you owe in total?

I = 5,000 × 0.08 × 3 = $1,200
Total owed: A = $5,000 + $1,200 = $6,200

Finding Other Variables

You can rearrange I = PRT to solve for any variable:

P = I / (R \times T)

R = I / (P \times T)

T = I / (P \times R)

Worked Example 3: Finding the Rate

You invested $3,000 and earned $360 in interest over 2 years. What was the interest rate?

R = I / (P × T) = 360 / (3,000 × 2) = 360 / 6,000 = 0.06
Convert to percent: 0.06 = 6%

Comparing Loan Options

Worked Example 4: Which Loan is Cheaper?

Option A: $10,000 at 6% for 4 years. Option B: $10,000 at 5% for 5 years.

Option A interest: 10,000 × 0.06 × 4 = $2,400
Option B interest: 10,000 × 0.05 × 5 = $2,500
Option A costs less in total interest, despite the higher rate, because of the shorter term.

Time Must Be in Years

If time is given in months, convert to years by dividing by 12. For example, 18 months = 18/12 = 1.5 years. If in days, divide by 365.

Simple vs. Compound Interest

Simple interest is calculated only on the original principal. It does not grow on the interest already earned. This makes it "simple" but also less realistic for long-term investments. Most bank accounts and loans use compound interest (covered in the next lesson).

Practice Problems

1. Calculate the simple interest on $800 at 5% for 3 years.

Show Solution

I = 800 × 0.05 × 3 = $120

2. You borrow $1,500 at 9% simple interest for 2 years. What is the total amount you repay?

Show Solution

I = 1,500 × 0.09 × 2 = $270. Total: $1,500 + $270 = $1,770.

3. An investment earned $600 in interest over 4 years at 5% simple interest. What was the principal?

Show Solution

P = I / (R × T) = 600 / (0.05 × 4) = 600 / 0.20 = $3,000

4. You invest $4,000 at 3.5% simple interest. How many years until you earn $700 in interest?

Show Solution

T = I / (P × R) = 700 / (4,000 × 0.035) = 700 / 140 = 5 years

5. Loan A: $6,000 at 7% for 3 years. Loan B: $6,000 at 5.5% for 4 years. Which costs less interest?

Show Solution

Loan A: 6,000 × 0.07 × 3 = $1,260. Loan B: 6,000 × 0.055 × 4 = $1,320. Loan A costs less ($1,260 vs. $1,320).

Lesson Summary

Simple interest: I = P × R × T. Total amount: A = P + I.
R must be a decimal; T must be in years.
Rearrange the formula to find any unknown variable.
When comparing loans, consider both the rate and the time period.