Game of Life
Every member of the family needs to get involved in sorting out the Jones’ financial year.
Robbie’s Dilemma
Robbie needs to raise £350 towards his season ticket.
He receives £25 a month from his paper round as standard.
Can he afford it at the end of the year?
However…
1.
2.
3.
4.
5.
6.
7.
8.
January:
February:
March:
April:
May:
June:
July:
August:
.
9. September:
.
10. October:
11. November:
.
12. December:
.
Robbie gets 10% extra
Robbie is poorly and loses 20% of his pay
Robbie spends 15% of his pay on a birthday present
Robbie picks up extra hours and earns 35% more
Robbie gets a permanent 20% pay rise
Robbie spends 8% of his pay on downloading music
Robbie gets a 13% bonus from delivering extra leaflets
Robbie earns 45% more for extra hours but then spends 15% of what
is left on clothes
Robbie spends 8% on downloads, then 18% of what is left on a . . . . .
present
Robbie is getting worried so does more hours to earn 37% more
Robbie spends 5% on his mum, 7% on his dad and 3% on his sister .
from his monthly pay for Christmas
Robbie gets a monthly pay rise of 3% and does extra hours at this
.
new rate to earn 20% more.
Oliver Jones
Oliver has recently inherited £12340.
He wants to invest the money for five years and is considering his investment options:
How much would each of the following give him at the end of five years?
Which would make him the most money?
1. Bank of Pi
2. Bank of Epsilon
3. Alpha Bank
Invest at an interest
rate of 4.3%
Invest the first £10000
at 4.5% and 3.7%
thereafter
Invest for the first year
at 5.6% and then at
3.8%
4. Share Save
5. TEMPTATION
6. Beta Bank
We promise to turn
your £12340
investment into
£15000 over five
years. What set
interest rate is
required?
Buy a new car!!
Spend all the money
but you would lose 8%
on the value during the
first year and 5% each
year after.
Invest with us and we
will give you a 3%
lump sum bonus for
the first year, as well
as a standard interest
rate of 3.95%
7. Options open…
8. Bank of doubling
9. Bank of rising %
Invest half in Alpha
and half in Beta
You can only invest
here at 7.6% if you are
willing to wait to
withdraw until your
money has doubled. Is
this doable in the five
year plan?
Year 1 = 2%
Year 2 = 3%
Year 3 = 4%
Year 4 = 5%
Year 5 = 6%
Mark Scheme
Robbie’s Dilemma
£25 a month standard and needs to raise £350
January: Robbie gets 10% extra
25 ÷ 10 = 2.50
25 x 1.1
25 + 2.50 = £27.50
= £27.50
25 x 0.1
25 + 2.50
= 2.50
= £27.50
DID YOU GET £2.50? Common Error - Working out the value and not adding it to the
original
February: Robbie is poorly and loses 20% of his pay
25 ÷ 10
= 2.50
25 x 0.8
= £20
25 x 0.2
= 5.00
2.50 x 2
= 5.00
25 – 5.00
= £20
25 – 5.00
= £20
DID YOU GET £5.00? Common Error - Working out the value and not subtracting it from the
original
DID YOU GET £18.75? Common Error – to find 20% you did 25 ÷ 20 = £1.25
March:
Robbie spends 15% of his pay on a birthday present
25 ÷ 10
= 2.50
25 x 0.85
= £21.25
25 x 0.15
= 3.75
2.50 ÷ 2
= 1.25
25 – 3.75
= £21.25
2.50 + 1.25 = 3.75
25 – 3.75
= £21.25
DID YOU GET £3.75? Common Error - Working out the value and not subtracting it from the
original
DID YOU GET £28.75? Common Error – adding the 15% - Robbie spent the money so
would have less left
April:
Robbie picks up extra hours and earns 35% more
25 ÷ 10
= 2.50
25 x 1.35
= £33.75
25 x 0.35
= 8.75
2.50 x 3
= 7.50
25 + 8.75
= £33.75
2.50 ÷ 2
= 1.25
7.50 + 1.25 = 8.75
25 + 8.75
= £33.75
DID YOU GET £8.75? Common Error - Working out the value and not adding it to the
original
May:
Robbie gets a permanent 20% pay rise
25 ÷ 10
= 2.50
25 x 1.2
= £30.00
25 x 0.2
= 5.00
2.50 x 2
= 5.00
25 + 5.00
= £30.00
25 + 5.00
= £30.00
DID YOU GET £5.00? Common Error - Working out the value and not adding it to the
original
Note – all calculations from now on should be from using £30 a month pay
June:
Robbie spends 8% of his pay on downloading music
30 ÷ 100
= 0.3
30 x 0.92
= £27.60
30 x 0.08
= 2.40
0.3 x 8
= 2.40
30 – 2.40
= £27.60
30 – 2.40
= £27.60
DID YOU GET £2.40? Common Error - Working out the value and not subtracting it from the
original
DID YOU GET £23? Common Error – Using the original £25 monthly pay rather than £30
July:
Robbie gets a 13% bonus from delivering extra leaflets
30 ÷ 100
= 0.3
30 x 1.13
= £33.90
30 x 0.13
= 3.90
0.3 x 13
= 3.90
30 + 3.90
= £33.90
30 + 3.90
= £33.90
DID YOU GET £3.90? Common Error - Working out the value and not adding it to the
original
DID YOU GET £28.25? Common Error – Using the original £25 monthly pay rather than £30
August:
Robbie earns 45% more for extra hours but then spends 15% of what is left
on clothes
30 ÷ 100
= 0.3
30 x 1.45
= 43.50
30 x 0.45
= 13.50
0.3 x 45
= 13.50
43.50 x 0.85 = £36.98
30 + 13.50
= £43.50
30 + 13.50
= £43.50
43.50 x 0.15 = 6.525
43.50 ÷ 100 = 0.435
43.50 – 6.525 = 36.975
0.435 x 15
= 6.525
= £36.98
43.50 – 6.525 = 36.975
= £36.98
DID YOU GET £39.00? Common Error - 45% more and then 15% decrease = 30% gain in
total. You cannot collate the percentages as the 15% loss calculated is from a new total, not
the original value
DID YOU GET £36.97 or £36.975? Common Error – not rounding correctly to 2dp (money)
in the final steps
Common Error - rounding 6.525 to 6.53 before subtracting from 43.50. Do not round until
last step.
September: Robbie spends 8% on downloads, then 18% of what is left on a present
30 ÷ 100
= 0.3
30 x 0.92
= 27.60
30 x 0.08
= 2.40
0.3 x 8
= 2.40
27.60 x 0.82 = £22.63
30 - 2.40
= £27.60
30 - 2.40
= £27.60
27.60 x 0.18 = 4.968
27.60 ÷ 100 = 0.276
27.60 – 4.968 = 22.632
0.276 x 18
= 4.968
= £22.63
27.60 – 4.968 = 22.632
= £22.63
DID YOU GET £22.20? 8% spent and then a further 18% decrease = 26% loss in total
You cannot collate the percentages as the 18% loss calculated is from a new total, not the
original value
October:
Robbie is getting worried so does more hours to earn 37% more
30 ÷ 100
= 0.3
30 x 1.37
= £41.10
30 x 0.37
= 11.10
0.3 x 37
= 11.10
30 + 11.10
= £41.10
30 + 11.10
= £41.10
DID YOU GET £11.10? Common Error - Working out the value and not adding it to the
original
November:
Robbie spends 5% on his mum, 7% on his dad and 3% on his sister from his
monthly pay for Christmas
30 ÷ 100
= 0.3
30 x 0.95
= £28.50
30 x 0.05
= 1.50
0.3 x 5
= 1.50
30 x 0.93
= £27.90
30 x 0.07
= 2.10
30 ÷ 100
= 0.3
30 x 0.97
= £29.10
30 x 0.03
= 0.90
0.3 x 7
= 2.10
1.50 + 2.10 + 0.90 = 4.50
1.50 + 2.10 + 0.90 = 4.50
30 ÷ 100
= 0.3
30.00 – 4.50 = £25.50
30.00 – 4.50 = £25.50
0.3 x 3
= 0.90
1.50 + 2.10 + 0.90 = 4.50
30.00 – 4.50 = £25.50
DID YOU GET £25.71? Common Error - To take each % from the new value calculated. I.e.
5% on mum leaves you with £28.50, and then calculate the 7% from this. In this case each
% is from his monthly pay so calculated individually.
December:
Robbie gets a monthly pay rise of 3% and does extra hours at this new rate to
earn 20% more.
30 ÷ 100
= 0.3
30 x 1.03
= 30.90
30 x 0.03
= 0.90
0.3 x 3
= 0.90
33.90 x 1.2
= £37.08
30 + 0.90
= 30.90
30 + 0.90
= 30.90
30.90 x 0.2
= 6.18
30.90 ÷ 100 = 0.309
30.90 + 6.18 = £37.08
0.309 x 20
= 6.18
30.90 + 6.18 = £37.08
DID YOU GET £36.90? Common Error- 3% more followed by a 20% increase = 23% gain in
total. You cannot collate the percentages as the 20% calculated is from a new total after the
pay rise and not the original value.
Calculate the total:
27.50 + 20 + 21.25 + 33.75 + 30 + 27.60 + 33.90 + 36.98 + 22.63 + 41.10 + 25.50 + 40.68
= £360.89
Robbie has enough money by £10.89
Mark Scheme
Oliver’s Choice
Oliver has recently inherited £12340.
He wants to invest the money for five years and is considering his investment options:
Bank of Pi: Invest at an interest rate of 4.3%
12340 x 1.0435
= 15231.29052
= £15231.29
DID YOU GET £14993.10? Common Error – 4.3 x 5 = 21.5% interest. 12340 x 1.215 =
14993.10 You cannot collate the percentages as each 4.3% calculated is from a new total,
not the original value
Bank of Epsilon: Invest the first £10000 at 4.5% and 3.7% thereafter
10000 x 1.0455
= 12461.81938
2340 x 1.0375
= 2806.14197
12461.81938 + 2806.14197 = 15267.961135
= £15267.96
DID YOU GET £15022.90? Common Error – 4.5 x 5 = 22.5% interest. 10000 x 1.225 =
12250. 3.7 x 5 = 18.5% interest. 2340 x 1.185 = 2772.9. 2772.9 + 12250 = £15022.90
You cannot collate the percentages as each % calculated is from a new total, not the original
value
Alpha Bank: Invest for the first year at 5.6% and then at 3.8%
12340 x 1.056
= 13031.04
13031.04 x 1.0384
= 15127.54634
= £15127.55
DID YOU GET £14906.72? Common Error – 5.6 + 3.8 x 4 = 20.8% interest. 12340 x 1.208 =
14906.72 = £14906.72 You cannot collate the percentages as each % calculated is from a
new total, not the original value
Share Save: We promise to turn your £12340 investment into £15000 over five years. What
set interest rate is required?
12340 x 𝑥 5
= 15000
15000 ÷ 12340
= x5
5
x
= 1.21559
5
= 1.039812
√1.21559
= 3.98% interest rate
TEMPTATION: Buy a new car!! Spend all the money but you would lose 8% on the value
during the first year and 5% each year after.
12340 x 0.992
= 12241.28
12241.28 x 0.9954
= 11998.28448
= £11998.28
DID YOU GET £8884.80? 8 + 5 x 4 = 28% loss. 12340 x 0.72 = 8884.8 = £8884.80
You cannot collate the percentages as each % loss calculated is from a new total, not the
original value
Beta Bank: Invest with us and we will give you a 3% lump sum bonus for the first year, as
well as a standard interest rate of 3.95%
12340 x 0.03
= 370.20
12340 x 1.03955
= 14977.44136
14977.44136 + 370.20
= 15347.64136
= £15347.64
DID YOU GET £15426.76? Common Error – 12340 x 1.03 = 12710.2. 12710.2 x 1.03955 =
15426.7641 = £15426.76 Note, the lump sum bonus is a one off payment and is not eligible
to any interest.
DID YOU GET £15147.35? Common Error – Lump Sum: 12340 x 0.03 = 370.20. 3.95 x 5 =
19.75% interest in total. 12340 x 1.1975 = 14777.15. 14777.15 + 370.20 = £15147.35
You cannot collate the percentages as each 3.95% calculated is from a new total, not the
original value
Options open…: Invest half in Alpha and half in Beta
12340 ÷ 2
= 6170
7673.820682 + 7563.773169 = 15237.59385
= £15237.59
BETA
ALPHA
6170 x 0.03
= 185.1
6170 x 1.056 = 6515.52
6170 x 1.03955
= 7488.720682
6515.52 x 1.0384 = 7563.773169
7488.720682 + 185.1 = 7673.820682
COMMON ERROR 1 – BETA BANK: 12304 ÷2 = 6170. 6170x 1.03 = 6355.1.
6355.1 x 1.03955 = 7713.382303. Note, the lump sum bonus is a one off payment and is not
eligible to any interest.
COMMON ERROR 2 – BETA BANK: 6170 x 0.03 = 185.1. 3.95 x 5 = 19.75% interest.
6170 x 1.1975 = 7388.575. You cannot collate the percentages as each 3.95% calculated is
from a new total, not the original value
COMMON ERROR 3 – ALPHA BANK: 5.6 + 3.8 x 4 = 20.8% interest. 6170 x 1.208 =
7453.36. You cannot collate the percentages as each % calculated is from a new total, not
the original value
Bank of doubling: You can only invest here at 7.6% if you are willing to wait to withdraw until
your money has doubled…Is this doable in the five year plan?
12340 x 2
= 24680
12340 x 1.0765
= 17798.2177
= £17798.22
No his investment has not doubled in five years
DID YOU SAY NO BECAUSE YOU ONLY GOT £17029.20? 7.6 x 5 = 38% interest.
12340 x 1.38 = 17029.2 = 17029.20. You cannot collate the percentages as each 7.6%
calculated is from a new total, not the original value
Bank of rising %: Year 1 = 2% Year 2 = 3% Year 3 = 4% Year 4 = 5% Year 5 = 6%
12340 x 1.02 x 1.03 x 1.04 x 1.05 x 1.06 = 15006.55692
= £15006.56
DID YOU GET £14808? Common Error: 2 + 3 + 4 + 5 + 6 = 20% interest.
12340 x 1.2 = 14808 You cannot collate the percentages as each % calculated is from a
new total, not the original value
The Best option is Beta Bank in the five year plan
SELF ASSESSMENT
DISCRETE GROWTH AND DECAY 5.03a
FOUNDATION
BASED ON ROBBIE’S DILEMMA
Topic
Questions
Calculate any %
ALL
Calculate % increases
1, 4, 5, 7, 10
Calculate % decreases
2, 3, 6
Calculate % with
multipliers
ALL
Calculate % increases
with multipliers
Calculate % decreases
with multipliers
Calculate repeated %
change with multipliers



Targets to Improve
1, 4, 5, 7, 10
2, 3, 6
8, 9, 11, 12
SELF ASSESSMENT
DISCRETE GROWTH AND DECAY 5.03a
HIGHER
BASED ON OLIVER’S CHOICE
Topic
Questions
Using % multipliers to
find a given %
Using % multipliers to
decrease values
Using % multipliers to
increase values
Calculate repeated %
change with multipliers
Compound Interest
formula for increases
Compound Interest
formula for decreases
Working backwards to
find interest rate
ALL
5
1, 2, 3, 6, 7, 8
9
1, 2, 3, 6, 7, 8
5
4



Targets to Improve