Compound Interest GCSE Questions, Worked Examples and Answers

Convert $7.2\%$ to a decimal and add it to $1$.

$7.2\%=\frac{7.2}{100}=0.072$

$1+0.072=\boxed{1.072}$

The multiplier is just above $1$, which is sensible for an increase.

The annual multiplier is

$1+\frac{2.8}{100}=1.028$

There are two annual interest periods, so use power $2$.

$A=850\times1.028^2$

Enter 850 × 1.028² using the power key, or enter 850 × 1.028 × 1.028.

$A=898.2664$

Round to the nearest penny only at the end.

$\boxed{A=\text{£}898.27}$

First find the final balance using multiplier $1.036$.

$A=1250\times1.036^3$

$A=1389.91832$

This is the balance, not the interest. Subtract the original £1,250.

$\text{interest}=1389.91832-1250$

$\text{interest}=139.91832$

Round once, at the end.

$\boxed{\text{Interest earned}=\text{£}139.92}$

For simple interest, $5\%$ of £900 is added each year.

$\text{simple yearly interest}=900\times0.05=45$

$S=900+2\times45=990$

For compound interest, multiply the changing balance by $1.05$ twice.

$C=900\times1.05^2$

$C=992.25$

Compare the final balances.

$992.25-990=2.25$

$\boxed{\text{Account C has £2.25 more.}}$

A quarter is 3 months, so first count the interest periods.

$18\div3=6\text{ quarters}$

The multiplier per quarter is

$1+\frac{1.1}{100}=1.011$

Use power $6$, not power $1.5$.

$A=2400\times1.011^6$

$A=2562.820417\ldots$

$\boxed{A=\text{£}2,562.82}$

The monthly multiplier is $1.007$, and it is applied eight times.

$A=3200\times1.007^8$

$A=3383.652406\ldots$

The question asks for the balance owed, so no subtraction is needed.

$\boxed{A=\text{£}3,383.65}$

Use one multiplier for each stage. Each rate is applied for two periods.

$A=5000\times1.024^2\times1.031^2$

Keep the calculation in one calculator line so the balance after the first stage is not rounded.

$A=5572.97696768$

$\boxed{A=\text{£}5,572.98}$

The two powers account for all four years: $2+2=4$.

Let the original investment be $P$. The growth model is

$4961.25=P\times1.05^2$

Undo multiplication by $1.05^2$ by dividing by the complete growth factor.

$P=\frac{4961.25}{1.05^2}$

$P=4500$

$\boxed{\text{Original investment}=\text{£}4,500}$

Check: $4500\times1.05^2=4961.25$.

Let $m$ be the annual multiplier.

$1984.50=1800m^2$

Divide by $1800$.

$m^2=\frac{1984.50}{1800}$

$m^2=1.1025$

Use the square-root key because there are two equal growth periods.

$m=\sqrt{1.1025}=1.05$

The increase is the part above $1$.

$r=(1.05-1)\times100=\boxed{5\%}$

Use multiplier $1.05$ and test consecutive whole-number powers near the target. No logarithms are needed.

After 3 years:

$2400\times1.05^3=2778.3$

This is below £2,900.

After 4 years:

$2400\times1.05^4=2917.215$

This is above £2,900. Because year 3 is still below the target, year 4 is the first time it is exceeded.

$\boxed{4\text{ years}}$

For Account A, there are three annual periods.

$A=4000\times1.033^3$

$A=4409.211748$

For Account B, 3 years is $3\times12=36$ monthly periods.

$B=4000\times1.0027^{36}$

$B=4407.7456877234986479\ldots$

Compare the unrounded balances, then round the difference.

$4409.211748-4407.7456877234986479\ldots=1.4660602765\ldots$

$\boxed{\text{Account A gives £1.47 more.}}$

Plan P adds the same $4\%$ of £3,600 each year.

$P=3600(1+5\times0.04)$

$P=4320$

Plan Q applies multiplier $1.04$ to each new balance.

$Q=3600\times1.04^5$

$Q=4379.95044864$

Both plans start with the same £3,600, so the difference between their final balances is also the difference between the interest earned.

$4379.95044864-4320=59.95044864$

$\boxed{\text{Plan Q earns £59.95 more interest.}}$

Apply the two growth stages before taking the fee.

$A=7200\times1.025^2\times1.018^3$

$A=7980.379810164$

The fee is a fixed amount, so subtract £35 after the compound calculation.

$7980.379810164-35=7945.379810164$

Round the money only after the final operation.

$\boxed{\text{Final amount}=\text{£}7,945.38}$

Noah has added four lots of $6\%$ of the original £2,100. That is a simple-interest calculation. With compound interest, each year’s percentage is applied to the new balance.

The annual multiplier is

$1+\frac{6}{100}=1.06$

Apply it four times.

$A=2100\times1.06^4$

$A=2651.201616$

$\boxed{A=\text{£}2,651.20}$

The power counts repeated multiplication; the rate itself is not multiplied by the number of years.