Azalea & Duncan each put
£2000 in their saving accounts.
They both got 5% interest per year.
Azalea withdrew the interest each year to
help with her bills.
Duncan deposited the interest back
into his savings account.
After 5 years, how much have they each spent/saved?
Year 1)
2000 × 0.05 = £100
Year 1)
2000 × 0.05 = £100
2)
2000 × 0.05 = £100
2)
2100 × 0.05 = £105
3)
2000 × 0.05 = £100
3)
2205 × 0.05 = £110.25
4)
2000 × 0.05 = £100
4)
2315.25 × 0.05 = £115.76…
5)
2000 × 0.05 = £100
5)
2431.01 × 0.05 = £121.55
Spent: £500
Savings Account: £2000
Savings Account: £2552.56
£100 is invested @ 10% interest per year
The interest is reinvested.
What would this look like in a graph?
£100
£10
£100
£110
£121
£133
£146
£161
£177
£195
£214
£236
£259
Value,
£
£11
Time
£12.10
£13.31
£14.64
£16.11
£1000 is invested @ 20% interest per year
The interest is reinvested.
After how many years is the money doubled?
£1031.96
When is the yearly interest the same as
the original amount?
Over double the investment
£2073.60
0
1
2
3
4
5
6
7
8
9
10
Repeated Percentage Change
John deposited $350 in a bank.
He earned 10% compound interest every year.
How much was in the account after 4 years?
1st Year =
350 × 1.1 = 385
2nd Year =
385 × 1.1 = 423.5
3rd Year =
423.5 × 1.1 = 465.85
4th Year = 423.5 × 1.1 = 512.435
Is there an easier method?
Multiplier:
= 100% + 10%
= 1.0 + 0.1
= 1.1
Repeated Percentage Change
John deposited $350 in a bank.
He earned 10% compound interest every year.
How much was in the account after 4 years?
1st Year =
2nd Year =
3rd Year =
350 × 1.1
(350 × 1.1) × 1.1
Multiplier:
= 100% + 10%
= 1.0 + 0.1
= 1.1
((350 × 1.1) × 1.1) × 1.1
4th Year = (((350 × 1.1) × 1.1) × 1.1) × 1.1 = $512.44
nth Year =
n
350 × 1.1
simplify
Formula:
Years
Quantity × Multiplier
Max deposited $312 in a bank.
He earned 17% compound interest every year.
𝑛
What is the formula for the total after
𝑛
312 × 1.17
Formula:
Years
Quantity × Multiplier
years?
Jenny deposited $10,400 in a bank.
She earned 0.8% compound interest every year.
What is the formula for the total after
𝑛
years?
𝑛
10400 × 1.008
Formula:
Years
Quantity × Multiplier
A 60 centimetre tall sampling is planted.
It grows by 7% every year.
What is the formula for the trees height after
𝑛
60 × 1.07
Is there a limit?
Formula:
Years
Quantity × Multiplier
𝑛
years?
A 20 centimetre long kitten grows by 4 cm in the first week.
What is the formula for kitten’s length after
𝑛
4
= 20%
20
60 × 1.2
Is there a limit?
Formula:
Period
Quantity × Multiplier
𝑛
weeks?
A virus has infected 3000 people in a city.
Every day 4% of the infected people infect another person.
What is the formula for
the total number of infected people after
𝑛
𝑛
3000 × 1.04
Formula:
Period
Quantity × Multiplier
days?
DEMO
Compound Interest
$370 is invested &
earns 30% interest per year.
How much is the
investment worth after 5 years?
period
370 × 1.35
principal
multiplier
= $1373.78
DEMO
YOUR TURN
Compound Interest
$520 is invested &
earns 7% interest per year.
$800 is invested &
earns 20% interest per year.
How much is the
investment worth after 6 years?
How much is the
investment worth after 4 years?
period
6
520 × 1.07
principal
4
800 × 1.2
multiplier
= $780.38
= $1658.88
DEMO
$520 is invested &
earns 7% interest per year.
YOUR TURN
Compound Interest
£700 invested for 4 years
1)
£1451.52
@ 20% interest p.a.
How much is the
investment worth after 6 years?
2)
£1200 invested for 3 years
£1641.16
@ 11% interest p.a.
3)
£820 invested for 7 years
@ 2% interest p.a.
4)
£1050 invested for 2 years
£1562.82
@ 22% interest p.a.
5)
£1770 invested for 6 years
£2731.64
@ 7.5% interest p.a.
6)
£12,000 invested for 8 years
@ 0.5% interest p.a.
£12488.48
period
6
520 × 1.07
principal
multiplier
= $780.38
7)
£1500 is invested
@ 7% interest p.a.
How many years until
the principal is doubled?
£941.92
11 years
A
£2000 is invested &
earns 15% interest per year.
B
How tall is the tree after
10 years?
How much is the
investment worth after 8 years?
C
A tree is 3 metres tall.
It grows by 4% every year.
2000 × 1.158
300 × 1.0410
= £6118.05
= 444.07 cm
Alice invests $850 in a company.
D
Tom invests $920 in a company.
Every year the value of the
company reduces by 5%.
Every year the value of the
company increases by 3.5%.
How much is Alice’s investment worth
after 3 years?
When is Tom’s investment worth
over $1100?
850 ×
0.953
= $728.77
920 × 1.035
𝐴𝑁𝑆 × 1.035
6 years
Mary invests £500 in a
savings account that offers 15% interest per year.
How many years does it take for Mary’s investment to be doubled?
15% of £500 = £75
500 ÷ 75 = 6.66
= 7 years
Do you agree?
How can we check?
Dave invests £4000 in a
savings account that offers 5% interest per year.
How many years does it take for Dave to earn £2000 from the investment?
5% of £4000 = £200
2000 ÷ 200 = 10
= 10 years
Do you agree?
How can we check?
How long until…
Using ‘Ans’
£5,000 invested at 12% interest per year is worth over £8,000?
Target = £8,000
1st input:
5000 × 1.12 = 5600
2nd input:
× 1.12 = 6272
3rd input:
= 7024.64
5 years
4th input:
= 7867.5968
5th input:
= 8811.708416
Using ‘Ans’
How long until…
£7,000 invested at 16% interest per year is worth over £10,000?
Target = £10,000
1st input:
7000 × 1.16 = 8120
2nd input:
× 1.16 =
3rd input:
= 10926.272
3 years
How long until…
Using ‘Ans’
£6,000 invested at 7% interest per year is worth over £9,000?
Target = £9,000
1st input:
2nd input:
3rd input:
4th input:
5th input:
6th input:
6000 × 1.07 = 6420
× 1.07 =
=
=
6 years
=
=
9004.38
How long until…
£560 invested at 4.5% interest per year earns £300?
Target = £860
1st input:
2nd input:
560 × 1.045 = 585.2
× 1.045 =
………
10 years
£869.66
Using ‘Ans’
How long until…
Using ‘Ans’
A) …£4,000 invested at 20% interest per year is worth over £9,000?
B) …£12,000 invested at 9% interest per year is worth over £20,000?
C) …a 60 cm tall sapling growing at 5% a month is over 1 metre tall?
D) …a 1.4 m tall bamboo plant growing at 12% a month is over 2.5 metres tall?
E) …a 4 day-old 10 cm tall baby chicken that grows by 30% a day is over 1 metre tall?
F) …£500 invested at 3.5% interest per year has earnt £200?
G) …an investment that gains 7% per year has doubled in value.
H) …an investment that loses 5% per year has halved in value.
Using ‘Ans’
How long until…
A) …£4,000 invested at 20% interest per year is worth over £9,000?
5 years
B) …£12,000 invested at 9% interest per year is worth over £20,000?
6 years
C) …a 60 cm tall sapling growing at 5% a month is over 1 metre tall? 11 months
D) …a 1.4 m tall bamboo plant growing at 12% a month is over 2.5 metres tall? 6 months
E) …a 4 day-old 10 cm tall baby chicken that grows by 30% a day is over 1 metre tall?
9 days
Never?
10 years
F) …£500 invested at 3.5% interest per year has earnt £200?
G) …an investment that gains 7% per year has doubled in value.
11 years
H) …an investment that loses 5% per year has halved in value.
14 years