Maths F4....23

22.
(Number of people aged 40 or above) > (Number of people aged below 40)
20000(1.003)^t > 22000(0.991)^t
(1.003/0.991)^t > 22000/20000
log(1.003/0.991)^t > log1.1
t*log(1.003/0.991) > log1.1
t > log1.1 / log(1.003/0.991)
t > 7.92

Since t is an integer, then t = 8
Hence, it is at least 8 years later.


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23.
(a)
Estimated monthly salary after 2 years
= $10000*(1 + 9%)^2
= $10000*(1.09)^2
= $11881

(b)
Estimated monthly salary after n years
= $10000*(1 + 9%)^n
= $10000*(1.09)^n

(c)
Estimated monthly salary after 5 years
= $10000*(1.09)^5
= $15386 (to the nearest integer)

After 5 years, the estimated salary is higher than $15000.
Hence, he can afford to buy a flat by instalments.