Foundation and Higher · compound interest

Compound interest
and depreciation.
Multiplier to a power.

interest on
the interest

each year builds on the last —

Compound

year 2 interest is on the new total

not on the original amount

step 1 of 4

Year by year

1. 3% increase: the multiplier is 1.03.

2. Multiply again for the next year.

✓ Same multiplier, again and again

each year: × 1.03

£2000 at 3% a year

2000

× 1.03

2060

× 1.03

2121.80

step 2 of 4

Use a power

1. Four years: multiply by 1.03 four times.

2. That is 1.03 to the power 4.

✓ Start × multiplier, to the power years

after 4 years

2000 × 1.03 × 1.03 × 1.03 × 1.03

= 2000 × 1.03⁴

= £2251.02

step 3 of 4

Depreciation

1. A 15% decrease leaves 85%: 0.85.

2. Same method, multiplier below 1.

✓ It falls by less each year

£12 000 car loses 15% a year

multiplier = 0.85

12 000 × 0.85³

= £7369.50 after 3 years

step 4 of 4

Not simple interest

1. Simple: the same £60 every year.

2. Compound interest grows each year.

✓ Read which one the question wants

£2000 at 3% for 4 years

simple: 60 × 4 = £240

compound: £251.02

compound earns more

compound change —

Multiplier

1.03 up, 0.85 down

Power

the number of years

Formula

start × multiplier^years

Interest only? Subtract
the starting amount at the end.

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