© t madas. £10000 are invested in a building society account. the account pays an annual interest...
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© T Madas
© 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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.This problem would be easy if banks/building societies paid SIMPLE INTEREST: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
6 x £800
£10000 + £4800
Is this what usually happens?
= £800
= £4800
= £14800
© T Madas
End of YearInterest CalculationStart of YearYear
1080010000 x 1.08100001
1166410800 x 1.08108002
15868.7414693.28 x 1.0814693.286
14693.2813604.89 x 1.0813604.895
13604.8912597.12 x 1.0812597.124
12597.1211664 x 1.08116643
This is what usually happens
© 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
Can you spot an easier calculation?
£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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.
© T Madas
Can you spot an easier calculation?
Originalamount
Interest increase as a % multiplier
years
£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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.
10000x 1.08( )x 1.08( )x 1.08( )x 1.08( )x 1.08( )x 1.08=
10000x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08=
10000x (1.08)6
© T Madas
Can you spot an easier calculation?
£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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.
10000x 1.08( )x 1.08( )x 1.08( )x 1.08( )x 1.08( )x 1.08=
10000x 1.08 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08=
remember the order of operations
10000 x1.586874 15868.74
=
=
10000x (1.08)6
© T Madas
© T Madas
( )7
£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
= 1407.10
( )15In 15 years:
1000 x 1.05
= 2078.93
( )25In 25 years:
1000 x 1.05
= 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 £10010 years earning £100 per yeargains £1000The investment doubles to £2000
Compound interest:
( )101000x 1.1 = 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
Compound interest:
In order for the £100 to double the investment must be worth £200 in n number of years( )n100x 1.05 = 200
This is an equation which requires logarithms to solve
We are going to use trial and improvement
How many years will it take £100 to double in value when invested at:
1. 5% simple interest
2. 5% compound interest
© T Madas
( )10100 x 1.05 = 162.89n = 10( )15100 x 1.05 = 207.89n = 15( )14100 x 1.05 = 197.99n = 14
Is the correct answer 14 or 15 years?
In order for the £100 to double the investment must be worth £200 in n number of years( )n100x 1.05 = 200
How many years will it take £100 to double in value when invested at:
1. 5% simple interest
2. 5% compound interest
Compound interest:
© T Madas