Answer:
After 13.4 years $80 will worth $40.
Step-by-step explanation:
If present value of an utensil is $80 then we have to calculate after how many years the same utensil will cost $40 with inflation rate of 5.4%.
If present cost of utensil is $80 then year by year cost of utensil with 5.4% inflation will form a geometric sequence as
$80, $75.68, $71.59, $67.72.........$40.
From this sequence we have to find number of term at which 40 comes.
In geometric sequence
[tex]T_{n}=a(r)^{n-1}[/tex]
Tn = 40
a = 80
r = common ratio = 75.68/80 = 0.946
[tex]40=80(.946)^{n-1}=(.946)^{n-1}=0.5[/tex]
By taking log on both the sides
log(0.5) = (n-1)log(0.946)
-0.301 = (n-1)(-0.0241)
n -1 = 0.301/0.0241 = 12.4
n = 12.5 + 1 = 13.4 years
Therefore after 13.4 years $80 will worth $40.
