Auczyt Com
et dealize
Solntion
a) The amount at the end of each year forms a GP, 0,01,
The first term, a=¢100000 and the common ratio, r= 1.08
Hence the second term is a=(100 000(1.08)=4108 000, which is the valne after 1 year
The third term is ar? =(100 000)(L08)2 = $116 640 which is the valve after 2 years,
and so on.
Therefore the value after 10 years='=(100 000) (1.08)!= 4205,890
b) When $300 000 has been reached, 300 000 ==> 300 000=100000(1.08)
3=(1.08) Taking logarithms to base 10 on both sides
log 3=log (1.08)
log 3=nlog (1.08)
log3
=143
log1.08
Hence it will take 15 years to reach more than $300 000
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