Paying to borrow, earning to save
Interest is the cost of borrowing money, or the reward for saving it. With simple interest, interest is calculated only on the original principal.
The formula
I = Prt
| Letter | Meaning |
|---|---|
| I | interest earned or paid |
| P | principal (starting amount) |
| r | annual interest rate, as a decimal |
| t | time in years |
The total amount is:
A = P + I = P(1 + rt)
Example: savings
Invest $2,000 at 3.5% per annum (per year) simple interest for 4 years.
- I = 2,000 × 0.035 × 4 = $280
- A = 2,000 + 280 = $2,280
Example: a loan
Borrow $5,000 at 7% simple interest for 18 months.
- t = 18/12 = 1.5 years
- I = 5,000 × 0.07 × 1.5 = $525
- Total to repay: $5,525
Time must be in years
| Given | t |
|---|---|
| 6 months | 0.5 |
| 9 months | 0.75 |
| 90 days | 90/365 ≈ 0.247 |
| 2 years 3 months | 2.25 |
Rearranging the formula
| Find | Formula |
|---|---|
| P | I ÷ (rt) |
| r | I ÷ (Pt) |
| t | I ÷ (Pr) |
Example: What rate earns $150 on $3,000 in 2 years?
r = 150 ÷ (3,000 × 2) = 0.025 = 2.5%
Growth is linear
Simple interest adds the same amount every year, so the balance grows in a straight line.
| Year | Balance ($1,000 at 5%) |
|---|---|
| 0 | $1,000 |
| 1 | $1,050 |
| 2 | $1,100 |
| 3 | $1,150 |
(Compound interest grows faster, because interest also earns interest.)
Where you’ll see simple interest
- Some short-term loans and car loans
- Some GICs that pay interest out each year
- Treasury bills and some bonds
Worked examples
Example 1: $800 at 4% for 3 years. Interest? $96.
Example 2: $1,200 at 6% for 8 months. Interest? 1,200 × 0.06 × (8/12) = $48.
Example 3: How long for $4,000 at 5% to earn $500? t = 500 ÷ 200 = 2.5 years.
Common mistakes
- Using the rate as a whole number (5 instead of 0.05).
- Using months instead of years for t.
- Giving only the interest when the question asks for the total amount.
Try it yourself
- $3,500 at 2.8% for 5 years. Interest?
- $10,000 at 6.5% for 9 months. Total amount?
- What principal earns $240 at 4% in 3 years?
- What rate turns $2,500 into $2,800 in 4 years?
Answers: 1) $490 2) $10,487.50 3) $2,000 4) 3%
Quick recap
- Simple interest: I = Prt.
- Amount = P + I.
- Use the rate as a decimal and time in years.