How do I find the lost opportunity of not investing an amount considering a certain inflation percent

I am doing a course on Personal Finance & Investment. In the chapter of about impact of not investing, one of the questions in a quiz is to calculate the effect of inflation on a sum of money not invested over a period of 2 years.

I calculated it using the formula:

``````impact_of_inflation = init_amt - init_amt * power(1 - inflation_rate/100, number_of_years)
``````

So, for an amount of 25000 with an inflation rate of 2.5% over a period of 2 years, it would be something like:

``````impact_of_inflation = \$25000 - \$25000 * power(1 - 2.5/100, 2) = \$1234.38
``````

However, the options given are \$1265.60, \$1556.20, \$1000.50 and \$1334.7

While the quiz is over and I passed based on the other questions, I am not sure how this is calculated. Can someone please help me understand how this works?

• I love how a quiz on personal finance seems to be suggesting that you should invest money needed within a two year time frame.
– user12515
Commented Nov 10, 2021 at 16:27

1 Answer

Well, you've got two problems -- a wrong formula, and a bad question.

The question is bad because it doesn't say whether you should give the present value or future value of the opportunity cost.

Opportunity cost of inflation is just the difference of two amounts, one of which has a PV of \$25000, the other has an FV of \$25000. So you can approach it either by finding FV(PV = \$25000), or PV(FV = \$25000). Both approaches are equally valid, and give two different numeric answers, and the question evidently expects you to read their mind to know which to report.

Your formula is wrong because discounting to present value is done as `pow(1 + rate, -time)` not `pow(1 - rate, time)` (naturally `rate` is `percent/100`)

The quantity `1 - rate` does appear in other cases such as tax-inclusive pricing, but not here.

• To clarify, \$25000 is the PV. We need to find the PV - FV. Commented Mar 10, 2019 at 21:02
• @KarthickS: If you fail to invest it, you will be left with (a smaller real amount) which has an FV of \$25000. You need to find the difference between these two real amounts (the opportunity cost). That loss can be expressed in either PV or FV. Commented Mar 10, 2019 at 21:06
• Thanks Ben. I am trying to find that opportunity cost. But the formula does not seem to work. Please guide me with the correct formula. Commented Mar 10, 2019 at 21:08
• Did you try with the correction I gave you? Commented Mar 10, 2019 at 21:08
• Yes. The answer comes to \$ 1204.64. It isn't one of the provided options. :( Commented Mar 10, 2019 at 21:11