Question

If the rate of inflation averages r per annum over n​ years, the amount A that​ $P will purchase after n years is Aequals​P(1minus​r)Superscript n​, where r is expressed as a decimal. If the average inflation rate is 4.8​%, how long is it until the purchasing power is cut in​ half?

Answer 1

14 years

Explanation:

here;

A = P(1-r)^n

we want to cut the purchasing power by half. What this means is that we will be making the amount half of what it used to be

what we want to calculate here is the value of n that makes A = P/2

r = 4.8% = 4.8/100 = 0.048

P/2 = P(1-0.048)^n

take off p from both sides

0.5 = 0.952^n

Take the log of both sides

log 0.5 = log 0.952^n

log 0.5 = n log 0.952

n = log 0.5/log 0.952 = 14.01

Which means the number of years is 14