GCSE Maths | Compound Interest
Final value = original value $\times$ multiplier$^{\text{(number of years)}}$
Worked Example
£1000 is invested at 4% per year for 3 years.
Multiplier $= 1.04$
Final value $= 1000 \times 1.04^3 = £1124.86$
Question 1
Find the total value after the given number of years, to the nearest penny.
a) £500 is invested at 5% compound interest per year for 3 years.
b) £1200 is invested at 3% per year for 4 years.
c) £800 grows at 4.5% per year for 5 years.
d) £1000 is invested at 2.5% per year for 2 years.
e) £2000 increases by 6% each year for 3 years.
f) £1500 is invested at 1.2% per year for 6 years.
g) £600 grows at 7% compound interest for 4 years.
h) £1800 increases by 2% a year for 10 years.
i) £100 grows at 10% interest per year for 3 years.
j) £2500 is invested at 3.5% per year for 8 years.
Show Answers
a) £578.81
b) £1350.61
c) £996.95
d) £1050.63
e) £2382.03
f) £1611.29
g) £786.48
h) £2194.19
i) £133.10
j) £3292.02
Worked Example
£900 depreciates at 20% per year for 3 years.
Multiplier $= 0.8$
Final value $= 900 \times 0.8^3 = £460.80$
Question 2
Find the value after the given number of years, to the nearest penny.
a) A car worth £12,000 depreciates at 10% per year for 3 years.
b) A laptop worth £800 loses 15% of its value each year for 2 years.
c) A phone bought for £1000 depreciates 20% annually for 4 years.
d) A machine costing £6000 depreciates at 5% per year for 5 years.
e) A sofa worth £1500 loses 12% of its value per year for 3 years.
f) A TV valued at £400 depreciates 25% a year for 2 years.
g) A bike costing £700 depreciates at 7% for 6 years.
h) A fridge bought for £300 depreciates 10% per year for 5 years.
i) A printer costing £500 loses 18% value annually for 3 years.
j) A used van worth £9000 depreciates by 8% a year for 4 years.
Show Answers
a) £8748.00
b) £578.00
c) £409.60
d) £4642.69
e) £1022.21
f) £225.00
g) £452.89
h) £177.15
i) £275.68
j) £6447.54
Worked Example
Naoby invests £6000 for 5 years. The investment gets compound interest of $x\%$ per annum. At the end of 5 years the investment is worth £8029.35. Work out the value of $x$.
$6000 \times x^5 = 8029.35$
Divide by 6000: $x^5 = 1.338225$
5th root both sides: $x = 1.06$
Convert the multiplier to a percentage: $x = 6$
Question 3
Each of the following investments grows for 5 years at a fixed annual compound interest rate. Find the interest rate in each case, correct to 1 decimal place.
a) £4000 grows to £4416.32 after 5 years.
b) £5500 grows to £6376.01 after 5 years.
c) £3000 grows to £3649.96 after 5 years.
d) £7200 grows to £9189.23 after 5 years.
e) £2500 grows to £2828.52 after 5 years.
f) £6000 grows to £7126.12 after 5 years.
g) £8000 grows to £9969.46 after 5 years.
h) £1500 grows to £2007.34 after 5 years.
i) £9000 grows to £9695.56 after 5 years.
j) £4800 grows to £6732.25 after 5 years.
Show Answers
a) $2.0\%$
b) $3.0\%$
c) $4.0\%$
d) $5.0\%$
e) $2.5\%$
f) $3.5\%$
g) $4.5\%$
h) $6.0\%$
i) $1.5\%$
j) $7.0\%$
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