Simple Interest
Lend money and you get paid for it; borrow it and you pay. Interest is that payment, worked out as a percentage of the amount per year. With simple interest the same amount is added every year, so the balance climbs in a straight line, and one formula covers everything.
National curriculum KS3: solve problems involving percentage change, including simple interest in financial mathematics. GCSE adds compound interest.1 · The same amount every year
Put £500 in an account paying 4% simple interest per year. Each year the bank adds 4% of the original £500, which is £20, and it's always £20: the interest already earned doesn't earn anything itself. After 1 year, £520; after 2, £540; after 10, £700. Drag the years and watch the bars grow by equal steps.
2 · The formula
Interest each year is P × R ÷ 100. For T years, multiply by T. That's the whole formula; the letters are the standard ones.
| Letter | Stands for | Unit | Watch out |
|---|---|---|---|
| I | Interest earned (or charged) | £ | The extra, not the total. Total = P + I. |
| P | Principal: the amount you start with | £ | |
| R | Rate of interest per year | % per year | Use the percentage number (4), the ÷ 100 is in the formula. |
| T | Time | years | 6 months is 0.5, not 6. Match the rate's unit. |
Any of the four can be the unknown. Cover the one you want and rearrange (see the rearranging formulae page): the other three tell you what to do.
Interest or total? Read the question twice. "How much interest does she earn?" wants I. "How much is in the account?" wants P + I. "How much does the loan cost him?" wants I. "How much does he pay back?" wants P + I. Half the marks lost on this topic are from answering the other question.
3 · It's a straight line
Because the same interest is added each year, total against time is a linear graph: y = mx + c with the principal as the intercept and the yearly interest as the gradient. Everything from the linear graphs page applies. Steeper line, higher rate.
4 · Simple versus compound (a preview)
Real savings accounts mostly pay compound interest: each year's interest is added to the balance, and next year's interest is a percentage of that bigger balance. Simple interest adds the same £20 every year; compound adds 4% of a growing number. Over a few years the gap is small; over decades it's enormous. The repeated-percentage-change idea from the previous page is exactly compound interest.
5 · Where simple interest is used
Short-term loans
Car finance and some personal loans quote a flat (simple) rate: borrow £6000 at 7% flat over 3 years and the interest is 6000 × 7 × 3 ÷ 100 = £1260, paid in equal instalments.
Bonds and savings certificates
A bond paying a fixed coupon each year is simple interest from the holder's point of view: same payment every year, principal back at the end.
Late payments
Statutory interest on an overdue invoice is charged as a daily simple rate: amount × rate × days ÷ 365. T doesn't have to be whole years.
Hire purchase
"£20 a month for 24 months" on a £400 item: you pay £480, so interest is £80 on £400 over 2 years: a simple rate of 10% a year. Working the rate out backwards is the R-unknown case.
Comparing offers
Two lenders, two rates, two terms: compute I for each and compare. The one with the lower rate isn't always cheaper if it runs for longer.
Spreadsheets
=P*R*T/100 in one cell, with P, R and T in their own cells, lets you change any input and watch the interest update: the formula as a live tool.
Worked examples
£1200 is invested at 3.5% simple interest for 4 years. Find the interest and the final amount.
How long does £2000 take to earn £300 at 5% simple interest?
A loan of £4500 costs £540 in interest over 2 years. What is the simple interest rate?
Exam-style: Priya invests £600 at 4% simple interest. Sam invests £600 at 4% compound interest. How much more does Sam have after 3 years?
Quick check
What you've learned
Simple interest adds the same amount every year: a fixed percentage of the original principal. I = PRT/100 gives the interest; the total is P + I. Any of the four letters can be the unknown, and rearranging finds it. Time must be in years to match a yearly rate. Plotted against time, simple interest is a straight line whose gradient is the yearly interest; compound interest, which you'll meet at GCSE, curves upward because each year's interest is a percentage of a growing balance.