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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 :

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

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

Here,

[tex]\begin{gathered} P=100 \\ r=0.025 \end{gathered}[/tex]

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

Then,

[tex]\begin{gathered} 600=100(1+0.025)^n \\ 6=(1.025)^n \end{gathered}[/tex]

Taking logarithm of both sides,

[tex]\begin{gathered} \ln 6=n\ln (1.025) \\ n=\frac{\ln 6}{\ln (1.025)} \\ \approx72.6 \end{gathered}[/tex]

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

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