Question

How long will it take for the dollar's purchasing power to be 3/4ths of what it is now, if the general inflation rate is expected to continue at 5%?

Answer 1

Answer:

5.61 years

Explanation:

Let the Present value be 'x'

Data provided in the question:

Future value = $\frac{3}{4}x$

Inflation rate, i = 5% = 0.05

Now,

Using the compounding

let number of years be n

thus,

Future value = Present value × [ 1 - inflation rate ]ⁿ

$\frac{3}{4}x$ = x × (1  - 0.05)ⁿ

or

0.75 = 0.95ⁿ

on taking log on both the sides , we get

or

log(0.75) = n × log(0.95)

or

-0.125 = n × (-0.0223)

or

n = 5.61 years

or, n = 11.89 years