© T Madas
£10000 are invested in a building society account.
The account pays an annual interest of 8%.
Calculate the amount in this account in 6 years time,
if no money is further paid in or withdrawn.
This problem would be easy if banks/building societies
paid SIMPLE INTEREST:
I.e. 8% on the original amount for every year
Then: 8% of £10000 = £800
6 x £800 = £4800
£10000 + £4800 = £14800
Is this what usually happens?
© T Madas
This is what usually happens
Year Start of Year Interest Calculation End of Year
1
10000
10000 x 1.08
10800
2
10800
10800 x 1.08
11664
3
11664
11664 x 1.08
12597.12
4
12597.12
12597.12 x 1.08
13604.89
5
13604.89
13604.89 x 1.08
14693.28
6
14693.28
14693.28 x 1.08
15868.74
© T Madas
This is known as the compound
interest calculation, when at the
end of a given period, say a year,
the “capital” and interest is
reinvested in a repetitive fashion
for a number of years.
© T Madas
£10000 are invested in a building society account.
The account pays an annual interest of 8%.
Calculate the amount in this account in 6 years time,
if no money is further paid in or withdrawn.
Can you spot an easier calculation?
© T Madas
£10000 are invested in a building society account.
The account pays an annual interest of 8%.
Calculate the amount in this account in 6 years time,
if no money is further paid in or withdrawn.
Can you spot an easier calculation?
((((( 10000 x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 =
10000 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 =
Original
amount
10000 x (1.08)6
years
Interest increase as a % multiplier
© T Madas
£10000 are invested in a building society account.
The account pays an annual interest of 8%.
Calculate the amount in this account in 6 years time,
if no money is further paid in or withdrawn.
Can you spot an easier calculation?
((((( 10000 x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 ) x 1.08 =
10000 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 =
10000 x (1.08)6 =
10000 x 1.586874 = 15868.74
remember the order of operations
© T Madas
© T Madas
£1000 were invested at a compound interest rate of
5% per annum.
Calculate the value of this investment in 7 years, 15
years and 25 years time.
In 7 years:
1000 x ( 1.05 )7 = 1407.10
In 15 years:
15
(
)
1000 x 1.05 = 2078.93
In 25 years:
1000 x (1.05 )25 = 3386.35
© T Madas
© T Madas
How much more does £1000 invested at 10%
compound interest for 10 years gain than
£1000 invested at 10% simple interest?
Simple interest: 10% of 1000 is £100
10 years earning £100 per year
gains £1000
The investment doubles to £2000
Compound interest: 1000 x (1.1)10 = 2593.74
an extra £593.74
© T Madas
© T Madas
How many years will it take £100 to double in
value when invested at:
1. 5% simple interest
2. 5% compound interest
Simple interest: 5% of 100 is £5
Every year £5 is earned
For the investment to double
another £100 must be gained
100 ÷ 5 = 20 years
© T Madas
How many years will it take £100 to double in
value when invested at:
1. 5% simple interest
2. 5% compound interest
Compound interest: In order for the £100 to double
the investment must be worth
£200 in n number of years
n
100 x ( 1.05 ) = 200
This is an equation which requires logarithms to solve
We are going to use trial and improvement
© T Madas
How many years will it take £100 to double in
value when invested at:
1. 5% simple interest
2. 5% compound interest
Compound interest: In order for the £100 to double
the investment must be worth
£200 in n number of years
n
100 x ( 1.05 ) = 200
n = 10
n = 15
n = 14
100 x (1.05 )10 = 162.89
100 x (1.05 )15 = 207.89
100 x (1.05 )14 = 197.99
Is the correct answer 14 or 15 years?
© T Madas
© T Madas