IGCSE Maths 0580 / Topic 1 / IGCSE

Interest on interest.

Simple interest adds the same amount every year. Compound interest adds a percentage of the growing total, so it earns interest on interest. The formulas are not given in the exam, so you need to know both.

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The key idea

Simple interest: $I = \dfrac{PRT}{100}$, the same every year. Compound interest: amount $= P\left(1 + \dfrac{r}{100}\right)^{n}$; subtract $P$ if the question asks for the interest only.

Fig. 1: $1000 invested at 10% per year. Simple interest adds $100 each year (a straight line); compound interest multiplies by 1.1 each year (a curve that pulls ahead)

Section 01

Simple interest.

In the lab, choose Simple and compound and set the rate and number of years. Watch the simple interest bars: each year adds exactly the same amount, because it is always worked out on the original sum.

Principal $P$: the amount invested or borrowed. Rate $R$: percentage per year. Time $T$: in years.
Simple interest $I = \dfrac{P \times R \times T}{100}$. The formula is NOT given in the exam.
Total amount $= P + I$. Read whether the question wants the interest or the total.

Worked example Simple interest

$\$2400$ is invested at 3.5% per year simple interest for 4 years. Find the total value at the end.

Interest $= \dfrac{2400 \times 3.5 \times 4}{100} = 336$.
Total $= 2400 + 336$.

Answer: $\$2736$

Worked example Finding the rate

$\$5000$ earns $\$750$ simple interest in 6 years. Find the rate of interest.

Rearrange: $R = \dfrac{100I}{PT}$.
$R = \dfrac{100 \times 750}{5000 \times 6} = \dfrac{75\,000}{30\,000} = 2.5$.

Answer: 2.5% per year

Your turn

How many years does it take for $\$2500$ to earn $\$500$ simple interest at 4% per year?

Examiner trap

Check whether the question asks for the INTEREST or the final AMOUNT. Giving $\$336$ when the total $\$2736$ was asked for loses the mark.

Section 02

Compound interest.

With compound interest the interest is added to the account each year, and next year's interest is worked out on the new total. The multiplier is applied once per year, so it is raised to the power of the number of years (Fig. 1).

Worked example Compound interest

$\$2400$ is invested at 3.5% per year compound interest for 4 years. Find (a) the final amount (b) the interest earned.

Multiplier for one year: $1.035$.
After 4 years: $2400 \times 1.035^{4} = 2754.055...$
Interest $= 2754.06 - 2400 = 354.06$.

Answer: (a) $\$2754.06$ (b) $\$354.06$, which is $\$18.06$ more than simple interest

Worked example How many years?

$\$1000$ is invested at 6% per year compound interest. After how many complete years will it first be worth more than $\$1500$?

Try values of $n$ in $1000 \times 1.06^{n}$.
$n = 6$: $1000 \times 1.06^{6} = \$1418.52$, not enough.
$n = 7$: $1000 \times 1.06^{7} = \$1503.63$, more than $\$1500$.

Answer: 7 years

Worked example Finding the rate (Extended)

$\$5000$ grows to $\$5832$ in 2 years at compound interest. Find the rate.

$5000 \times m^{2} = 5832$, where $m$ is the yearly multiplier.
$m^{2} = 5832 \div 5000 = 1.1664$.
$m = \sqrt{1.1664} = 1.08$.

Answer: 8% per year

Examiner trap

Compound interest is NOT the simple interest for one year multiplied by the number of years. $2400 \times 1.035 \times 4$ is meaningless; the power goes on the multiplier: $2400 \times 1.035^{4}$.

Stage 1 · Learn

Check your understanding

Four quick checks. Each correct answer earns XP and records this skill on your profile.

Quick check+10 XP

Find the simple interest on $\$500$ at 4% per year for 3 years.

Quick check+10 XP

Which calculation gives the value of $\$P$ after 3 years at 5% compound interest?

Quick check+10 XP

$\$200$ is invested at 10% per year compound interest. What is it worth after 2 years?

Quick check+10 XP

Same principal, same rate, 5 years. Which earns more interest?

Section 03

Comparing accounts.

To compare offers, work out each total for the same principal and time, then compare. A higher simple rate can still lose to a lower compound rate over enough years.

$\$6000$ for 6 years	Interest
4.5% simple	$6000 \times 0.045 \times 6 = \$1620$
4.2% compound	$6000 \times 1.042^{6} - 6000 = \$1679.94$

Examiner trap

Do not round the multiplier or round year by year. Keep the full calculator value and round only the final money answer to the nearest cent.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written to IGCSE Paper 2 and Paper 4 standard.

Finish the four checks above to unlock the exam questions

Exam style+20 XP

$\$3000$ is invested at 2.5% per year compound interest. How much interest is earned in 3 years?

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An amount is invested at 4% per year simple interest. After 5 years the interest is $\$340$. What amount was invested?

Exam style+20 XP

(Extended) $\$8000$ grows to $\$8820$ in 2 years at compound interest. What is the annual rate?

Exam style+20 XP

$\$4000$ is invested at 3% per year compound interest. After how many complete years is it first worth more than $\$4500$?

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Simple and compound interest, sorted.

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Go deeper · practice

Six original Cambridge-style questions

Simple and compound interest, finding the time and the rate, comparing two banks and counting years to a target.

\(\$6000\) for 6 years	Interest
4.5% simple	\(6000 \times 0.045 \times 6 = \$1620\)
4.2% compound	\(6000 \times 1.042^{6} - 6000 = \$1679.94\)