A number of personal finance blogs carry calculators which are based in Excel to evaluate portfolios and strategies. Millennials, on the other hand, go further and use coding in Python/R/qdb/whatnot and do fancier stuff to manage their finances. But is personal finance so hard and impossible to do without any computing? If yes, did no one in the generations gone by manage their finances well? If someone proposes to sell a complicated product with several money in-flows and payouts, how do we evaluate it without any computing tools?

The truth is it does not take high-end mathematics to manage personal finance. Most often, just two things will do – knowing to calculate interest, and understanding discounting. Anything beyond this is fancy.

Interest:
A principal of ₹ over a time years, earns a simple interest , if the bank offers an interest rate . However usually banks offer compounding, that is, the interest earned is reinvested as principal for the next year. In such a case, the principal for year 2 is and the interest earned on this during the second year is . The principal at the end of second year is then . Continuing this argument, for a timeframe of years, the compound interest is: .

Discounting:
To manage one’s personal finance, it is very important to distinguish between money and value. In economics, money (rupee notes as we touch it) is called fiat currency, where fiat is Latin for “it shall be”. What does that mean? Imagine the government printing notes and announcing, “This shall be your currency for transactions” to the people. The money is not linked to any commodities or gold, and the govt. can exercise its right to print as and when it likes.

When govt. prints notes as per its whims, the money that we hold today might not have the same value tomorrow. Discounting comes in handy to calculate this value – eg, the value of ₹1 held 50 years back in today’s terms. And similarly, to calculate the future value (say 50 years from now) of the ₹1000 note that I hold today. The calculation is closely related to compounding. This is because banks usually offer an interest rate that closely mirrors the rate of price increase (called inflation).

Imagine your grandfather had skipped a hotel lunch one day 50 years back and instead saved the lunch money of ₹1 in a bank. If he withdraws the money today, then the amount he would receive from the bank will fetch him a lunch today (likely a bit more, because the bank will reward him for holding out for such a long time). In other words, saving in a bank will cover price rise, without actually building your wealth (aka enhancing your purchasing power).

Looking forward, how do we use compounding to compute the future value of a ₹1000 note in our wallet today? Assume banks offer an interest rate of 5%, and will be doing so for the next 50 years. For a principal of ₹1000, and time period of 50 years, the interest earned is ₹, and the total amount, together with the principal is ₹. Imagine dishing out ₹12000 for a lunch during your retirement! This is why it is of utmost importance to plan one’s retirement and ensure today’s salary contributes to that lunch in the distant future.

A small caveat in the above discussion is the assumption of 5% interest rate. Usually as countries become developed, the rates stabilise at 1-2%. In India, the rates have declined from 20% to 7% over the last 25 years or so. If the interest rates become lower, then the prices of commodities and services wouldn’t rise as much. And that lunch will not be so expensive after all!