Question

How much money will you need to accumulate to maintain wealth if the inflation rate averages 3% per year for the next ten years?

Answer 1

The question, in other words, asks us to calculate the future value of the wealth, which is there at present.

For example, if you own $100 today, which can buy certain number of articles. If you want to buy the same number of articles, you would have to pay a greater amount of money, because there is inflation in the economy and the articles will become costlier as the time passes.

So, using the present value of money formula, and using the inflation rate as the discounting rate, we can find the future value of the $100 owned today, so that the purchasing power of today's $100 is equal to the future value 10 years hence.

Let the Future Value be FV

Present Value = PV = $100 (let's assume the wealth is $100, for easy calculations)

Discounting Rate = r = Inflation rate = 3%

No. of discounting periods = n= 10 (because annual inflation for 10 years is given to us)

So, FV = PV (1 + r)ⁿ

=> FV = 100 x (1 + 3%)¹⁰

=> FV = 100 x (1 + 0.03)¹⁰

=>FV = 100 x 1.343916 = 134.3916 = $134.39

Amount to be accumulated to maintaine wealth = FV - PV = 134.39 - 100 = $34.39

For every $100 of wealth owned today, I need to accumulate $34.39, to maintain my wealth. If I accumulate less than that, my wealth's purchasing power will erode.

In other words, I need to accumulate atleast 34.39% of my current wealth over the 10 years, so as to maintain the wealth. If I accumulate more than 34.39%, then it will increase my wealth.