Simple interest is calculated on the original amount only, every time period. The formula is I = PRT ÷ 100, where P is the principal (starting amount), R is the annual rate (%), and T is the time in years. The total amount is then A = P + I.
What does each letter in the formula stand for?
The formula I = PRT ÷ 100 uses four quantities:
| Letter | Stands for | Units | Example |
|---|---|---|---|
| I | Interest earned or paid | £ (or same currency as P) | £150 |
| P | Principal (starting amount) | £ | £2000 |
| R | Annual interest rate | % | 3 |
| T | Time | Years | 2.5 |
The ÷ 100 is needed because R is given as a percentage. Alternatively, write the formula as I = P × (R/100) × T, which makes the percentage-to-decimal conversion explicit.
How do you calculate the interest earned?
Worked example 1: £500 is invested at a simple interest rate of 4% per year for 3 years. How much interest is earned?
- P = 500, R = 4, T = 3
- I = (500 × 4 × 3) ÷ 100 = 6000 ÷ 100 = £60
Worked example 2: Calculate the interest on a loan of £1200 at 7% per annum for 18 months.
Note: T must be in years. 18 months = 1.5 years.
- P = 1200, R = 7, T = 1.5
- I = (1200 × 7 × 1.5) ÷ 100 = 12 600 ÷ 100 = £126
How do you find the total amount after simple interest?
The total amount is the principal plus the interest: A = P + I
Using the example above (£500 at 4% for 3 years):
- I = £60
- Total amount = 500 + 60 = £560
You can also write this in one step: A = P(1 + RT/100). However, at KS3 the two-step method (find I, then add to P) is clearer.
How do you rearrange the formula to find P, R or T?
The formula I = PRT/100 can be rearranged to find any unknown:
| Unknown | Rearrangement |
|---|---|
| Interest (I) | I = PRT ÷ 100 |
| Principal (P) | P = 100I ÷ (RT) |
| Rate (R) | R = 100I ÷ (PT) |
| Time (T) | T = 100I ÷ (PR) |
Worked example 3: Simple interest of £90 is earned on a principal of £600 over 3 years. Find the annual interest rate.
R = 100I ÷ (PT) = (100 × 90) ÷ (600 × 3) = 9000 ÷ 1800 = 5%
Worked example 4: How many years does it take £800 to earn £160 in simple interest at 5% per annum?
T = 100I ÷ (PR) = (100 × 160) ÷ (800 × 5) = 16 000 ÷ 4000 = 4 years
How does simple interest compare to compound interest?
At GCSE you will also study compound interest, which is calculated on the total accumulated (principal + interest already earned) rather than on the principal alone. Simple interest grows in a straight line; compound interest grows in a curve that accelerates over time.
| Year | Simple interest (5%, P = £1000) | Compound interest (5%, P = £1000) |
|---|---|---|
| 0 | £1000 | £1000 |
| 1 | £1050 | £1050.00 |
| 2 | £1100 | £1102.50 |
| 3 | £1150 | £1157.63 |
| 5 | £1250 | £1276.28 |
| 10 | £1500 | £1628.89 |
The gap widens significantly over longer periods. For short-term calculations at KS3, simple interest is the focus; compound interest is the GCSE extension.
What real-life situations use simple interest?
Simple interest is used in some short-term loans, hire-purchase agreements and savings bonds. In practice, most bank accounts and mortgages use compound interest, but simple interest is a good introduction to the concept and features regularly in KS3 exam questions.
Frequently asked questions
Why must T be in years when using I = PRT ÷ 100?
Because R is an annual rate (per year). If T is in months, the annual rate would be applied for a fraction of a year, giving too much interest. Always convert months to years before substituting (divide the number of months by 12). For example, 9 months = 9/12 = 0.75 years.
What if the interest rate is given monthly or weekly?
Check the units carefully. If R = 2% per month and T = 6 months, substitute directly because both R and T share the same time unit — there is no need to convert to years. The answer is then interest earned over those 6 months: I = P × 2/100 × 6. Always make sure R and T measure the same time period.
Is simple interest always the same each year?
Yes. That is the defining feature of simple interest: the same fixed amount of interest is added every period, because R is always applied to the original principal P, never to a growing total. This makes it linear — each year adds an identical amount.
How does simple interest relate to percentage calculations?
Simple interest for 1 year is just a percentage of the principal: I = P × R/100. This is exactly the "find a percentage of an amount" skill. Simple interest over T years multiplies that single-year interest by T. So all your percentage skills transfer directly into simple interest questions.
For personalised KS3 number and finance practice — visit aitutors.me.