SOLUTION: Adam’s annual salary is RM120,000 and his total expenses is RM90,000. His salary increases by RM12,000 each year while his expenses increase by RM15,000 each year. Each year, he

Question 1201145: Adam’s annual salary is RM120,000 and his total expenses is RM90,000. His salary increases
by RM12,000 each year while his expenses increase by RM15,000 each year. Each year, he
saves the excess of his income.
a) Represent his total savings as series.
b) If Adam continues to manage his finances this way, after how many years will he has
nothing left to save?
c) Adam calculates that if his expenses increase by 𝑥 RM every year (instead of RM15,000
each year), he will spend as much as he earns in the 25th
year. Determine 𝑥.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

Adam’s annual salary is RM120,000 and his total expenses is RM90,000.
His salary increases by RM12,000 each year while his expenses increase by RM15,000 each year.
Represent his total savings as series.
(120000-90000)+(144000-105000)+(156000-120000)....
(120000+144000+156000)... -(90000+105000+120000)...
Let n be the number of years when income = expenses
Both are arthimatic sequences
Tn= a+(n-1)d
a=120000
d =12000
tn= 120000 +(n-1)12000
= 108000 +12000n
Expense after n years
Tn= 90000+(n-1)15000
= 75000+15000n
Income = expense
108000 +12000n=75000+15000n
3000n =33000
n=11 Eleventh year there is no saving
Let x be the expence increase every year
number of years = 25 when saving is nil
T25= 120000 +(25-1)12000
= 120000 +288000
= 408000
408000 = 90000 +(25-1)x
408000 - 90000=24x
318000=24x
x= 13250 expence increase every year

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