lesson
The same starting amount each year
1 · Learn
Interest is an amount added to savings or charged on borrowing. Here we use an invented SIMPLE-interest model, not a real financial offer. The principal is the starting amount. With simple interest, each year's interest is calculated from that original principal, even after interest has been added.
For £200 at 5% per year, first find 1%: £200 ÷ 100 = £2. Five lots give £10 per year. After three years the interest is 3 × £10 = £30 and the total is £230. Do not calculate 5% of £210 in year two: that would change the agreed model.
For principal P, annual percentage rate r and time t in years, interest I = P × r/100 × t. Total A = P + I. Keep interest and total separate, and use years consistently. This model assumes no fees, repayments or extra deposits.
2 · Worked example
An invented £400 loan uses 3% SIMPLE interest per year for two years with no repayments. Annual interest is 400 × 0.03 = £12. Two years add £24, so the amount due is £424. Check: £24 is 6% of the original £400, not 6% of £424.
3 · Your turn
In this same simple-interest model, £300 is saved at 4% per year for three years. Find one year's interest, all the interest and the final total.
Check your answer
£12 per year; £36 interest over three years; £336 total. Each £12 is calculated from the original £300.
4 · Apply your learning
Draw a table for years 0, 1, 2 and 3 for the £300 example. Plot year against total, label both axes and explain why the increases are equal. This is a model calculation, not a financial recommendation.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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