Suppose that inflation is 2.5%

Question

per year. This means that the cost of an item increases by 2.5%
each year. Suppose that a jacket cost $65
in the year 2022.
How long will it take for the jacket to cost $150?

Answer 1

Let's use the formula for compound interest to solve this problem:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^number of years

In this case, FV is the final cost of the jacket ($150), PV is the initial cost ($65), the interest rate is the inflation rate (2.5%), and we want to solve for the number of years it takes to reach $150.

150 = 65 * (1 + 0.025)^number of years

Divide both sides by 65:

2.3077 = (1.025)^number of years

To isolate the "number of years," we can take the natural logarithm (ln) of both sides:

ln(2.3077) = ln((1.025)^number of years)

Using the logarithmic property, we can move the "number of years" to the front:

ln(2.3077) = number of years * ln(1.025)

Now, divide by ln(1.025) to solve for the "number of years":

number of years = ln(2.3077) / ln(1.025)

number of years ≈ 18.85

It will take approximately 18.85 years for the jacket to cost $150 with an inflation rate of 2.5% per year.