Problema Solution
If the rate of inflation averages r per annum over n years, the amount A that $P will purchase after n years is A=P(1r)^n, where r is expressed as a decimal.
If the average inflation rate is 3.8%, how long is it until the purchasing power is cut in half.
Answer provided by our tutors
For an annual inflation rate of r%, the amount A that $P will purchase after n years is
A = P(1-r)^n
r = 0.038
n = ?
A = P/2
P/2 = P(1-r)^n
P(1-r)^n = P/2 divide both sides by P
(1-r)^n = 1/2
(1 - 0.038)^n = 0.5
0.962^n = 0.5
ln 0.962^n = ln 0.5
n ln 0.962 = ln 0.5
n = ln 0.5 / ln 0.692
n = 1.883 years
1.883 years are needed for the purchasing power to be cut in half.