Cambridge International Mathematics

222 Topics in arithmetic (Chapter 10)

10 What is the overall effect of:

a increases of8%,9%and12%over three consecutive years

b decreases of3%,8%and6%over three consecutive years

c an increase of5%over four consecutive years?

11 Joshua’s wages increase by 3 :2%, 4 :8%and 7 :5%over three consecutive years. What is his overall

percentage increase over this period?

12 Jasmin’s income increases by11%, decreases by7%, increases by2%, and then increases by14%over

four consecutive years. What is her overall percentage increase for this four year period?

If you bank$1000, then you are actually lending the money to the bank. The bank in turn uses your money

to lend to other people. While banks pay you interest to encourage your custom, they charge interest to

borrowers at a higher rate. That way the banks make a profit.

If you leave the money in the bank for a period of time, the interest is automatically added to your account

and so the principal is increased. The next lot of interest will then be calculated on the higher principal.

This creates acompoundingeffect on the interest as you are gettinginterest on interest.

Consider an investment of$1000with interest of6%p.a. paid each year and compounded.

After year Interest paid Value

0 $1000: 00

1 6%of$1000:00 = $60: 00 $1000:00 + $60:00 = $1060: 00

2 6%of$1060:00 = $63: 60 $1060:00 + $63:60 = $1123: 60

3 6%of$1123:60 = $67: 42 $1123:60 + $67:42 = $1191: 02

We can usechain percentage increasesto calculate the account balance after 3 years.

Each year, the account balance is106%of its previous value.

) future value after 3 years = $1000£ 1 : 06 £ 1 : 06 £ 1 : 06

= $1000£(1:06)^3

= $1191: 02

Example 19 Self Tutor

$5000is invested at8%p.a. compound interest with interest calculated annually.

a What will it amount to after 3 years? b Find the interest earned.

a The multiplier is 108% = 1: 08

) value after 3 years = $5000£(1:08)^3

= $6298: 56

b Interest earned= $6298: 56 ¡$5000

= $1298: 56

F COMPOUND GROWTH [1.8]

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Y:\HAESE\IGCSE01\IG01_10\222IGCSE01_10.CDR Tuesday, 23 September 2008 3:36:29 PM PETER