© 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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.This problem would be easy if banks/building societies paid SIMPLE INTEREST: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

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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

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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.

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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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.

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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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.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

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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Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.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

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© 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

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© 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

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© 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

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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

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( )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:

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