Question

According to the rule of 72, in about how many years will $80 be worth $40 if the rate of inflation is 5.4%?

Answer 1

Answer: In about 7 to 8 years

Step-by-step explanation: If you subtract $80 with 5.4 8 times you get $42.2

Answer 2

After 13.4 years $80 will worth $40.

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

`T_(n)=a(r)^(n-1)`

Tn = 40

a = 80

r = common ratio = 75.68/80 = 0.946

`40=80(.946)^(n-1)=(.946)^(n-1)=0.5`

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.