Simple and Compound Interest

طریقہ، مرحلہ وار

1. 1

   Simple interest: multiply, then multiply again

   £2000 at 4% simple for 3 years → 2000 × 0.04 × 3 = £240 interest

   One year's interest is the principal times the rate; three years is that times three. The balance grows in a straight line, because the interest is always computed from the same starting figure no matter how much has accumulated.

2. 2

   Compound interest: raise the multiplier to a power

   £2000 at 4% compound for 3 years → 2000 × 1.04³ = £2249.73

   Each year multiplies the balance by 1.04, so three years multiplies by 1.04 three times. Writing it as a power rather than three separate multiplications is what makes twenty-year questions tractable.

3. 3

   Subtract the principal to isolate the interest

   £2249.73 − £2000 = £249.73 interest

   The compound formula returns the total balance, not the interest earned. Questions ask for one or the other and students routinely give the wrong one, which is a lost mark on an otherwise correct calculation.

4. 4

   Depreciation is compound decrease

   £18,000 car losing 15% a year for 4 years → 18000 × 0.85⁴ = £9396.11

   Nothing about the method changes; the multiplier is simply below 1. Depreciation questions are compound interest questions with a different story attached, and recognising that removes them as a separate topic.

5. 5

   Compare the two to see the gap

   3 years at 4%: simple £240, compound £249.73. At 20 years: £1600 vs £2382

   The difference is small over a few years and large over many, which is the entire point of the topic. Questions frequently ask students to compare the two, and the answer should always be that compound wins by more the longer it runs.

What actually differs

Simple interest is always computed from the original sum. Compound interest is computed from whatever is in the account now, which includes interest already earned. That single difference is why one grows in a straight line and the other curves upward, and why the gap widens with time rather than staying fixed.

Almost all real financial products compound — savings accounts, mortgages, credit cards, loans. Simple interest survives mainly as a teaching device and in a few short-term arrangements, which is worth telling students so they know which one describes the world they will live in.

• Simple: interest on the original amount, every period
• Compound: interest on the current balance
• Simple total = P × r × t
• Compound balance = P × (multiplier)^t
• Depreciation = compound with a multiplier below 1

Balance or interest — read the question

The compound formula gives the amount in the account, and a large share of lost marks come from handing that in when the question asked how much interest was earned. The two differ by exactly the principal, and the fix is one subtraction that takes three seconds.

We teach students to underline which one the question wants before starting. It sounds trivial; it is worth roughly a mark per compound-interest question across a paper.

Why compound interest is a lesson about time

At three years the difference between simple and compound at 4% is under ten pounds. At twenty years it is nearly eight hundred. The gap is not caused by the rate but by the number of times the interest is allowed to earn interest, and that is the genuinely useful idea in the topic.

It is also the idea behind the exam questions that ask how many years until a balance passes some threshold. Those are solved by trial with the multiplier, and students who understand why the growth accelerates make far better first guesses.

How we teach interest

We teach compound interest as repeated percentage increase rather than as a new formula. A student who is fluent with multipliers already knows how to do this, and presenting it as a formula to memorise discards that fluency and invites the formula to be misremembered.

We use real figures — actual savings rates, actual car depreciation — because the topic is one of the few in GCSE maths with immediate use outside the exam, and students engage with it differently once that is obvious.