Question

Suppose that inflation is 2.5% per year. This means that the cost of an item increases by 2.5% each year. Suppose that a jacket cost $100 in the year 2017.How long (in yr) will it take for the jacket to cost $600? Round your answer to the nearest year.

Answer 1

Given that the cost of an item increases by 2.5% each year.

Suppose that a jacket cost $100 in the year 2017.

Here,

`\begin{gathered} P=100 \\ r=0.025 \end{gathered}`

Suppose after n years, the cost of the jacket will be $600.

Then,

`\begin{gathered} 600=100(1+0.025)^n \\ 6=(1.025)^n \end{gathered}`

Taking logarithm of both sides,

`\begin{gathered} \ln 6=n\ln (1.025) \\ n=(\ln 6)/(\ln (1.025)) \\ \approx72.6 \end{gathered}`

By rounding to the nearest year, after 73 years the cost of the jacket will be $600.