Time Value of Money — For Kids

When I was kid, a friend made me a hypothetical proposition. He told me he would give me a Maruti 800 car every day (guess that was the fanciest car both of us were aware of at that age and time). In return, I would have to give Re 1 on the first day, Rs 2 on the second day, Rs 4 on the third day and so on for 30 days. I believe the car cost Rs 1 lac at the time. To put it in a different way, the deal was this:

  • I pay Re 1 to get Rs 1 lac on the first day.
  • I pay Rs 2 to Rs 1 lac on the second day.
  • I pay Rs 4 to Rs 1 lac on the third day.

And so on for 30 days. I had to pay double the amount I had paid the day before. To me, it looked like a good deal. I told my friend that I would happily take it. What would you have done? Who do you think will come out on top? My friend or I? Let’s do the math.

DayWhat I getWhat I pay
11,00,0001
21,00,0002
31,00,0004
41,00,0008
51,00,00016
61,00,00032
71,00,00064
81,00,000128
91,00,000256
101,00,000512
111,00,0001,024
121,00,0002,048
131,00,0004,096
141,00,0008,192
151,00,00016,384
161,00,00032,768
171,00,00065,536
181,00,0001,31,072
191,00,0002,62,144
201,00,0005,24,288
211,00,00010,48,576
221,00,00020,97,152
231,00,00041,94,304
241,00,00083,88,608
251,00,0001,67,77,216
261,00,0003,35,54,432
271,00,0006,71,08,864
281,00,00013,42,17,728
291,00,00026,84,35,456
301,00,00053,68,70,912

This is power of compounding in full flow. For Rs 1 lac on the 30th day, I will have to pay Rs 53.6 crores. For those 30 Maruti 800s, I would have to pay Rs 107.3 crores. A very bad deal for me. Clearly, my friend had outsmarted me. Another point to note: My friend knew the math. I didn’t. Our minds are not capable of processing such complex calculations without pen and paper. At least mine is not. Therefore, in life, do not rush to fall for these seemingly attractive offers.

How Long Does It Take to Double Your Money?

Let’s say you have Rs 1,000 with you. How long will it take for it become Rs 2,000? Clearly, a very long time but how long. If you keep it in cash, it will never become Rs 2,000. It will remain Rs 1,000 for eternity. If you keep it a savings account that earns you 4%, your investment will double in 17.6 years. If you keep it in a fixed deposit that gives 8% p.a., your investment will double in approximately 9 years. If you keep it in a fixed deposit that gives 12% p.a., your investment will double in 6.11 years. 

Had you kept your investment of Rs 1,000 in a 12% fixed deposit for 17.6 years (for the time where your investment doubles in your savings account at 4% p.a.), it would have become Rs 7410. Contrast this: Rs 2,000 in 17.6 years (at 4%) vs Rs 7,410 in 17.6 years (at 12%). Now, let’s increase the investment horizon to 30 years. At 4%, your money will grow to Rs 3,243. At 12%, your money will grow to Rs 29,959. Now, this amount is 9 times the corpus at 4%.

The different in amounts may not be stark to begin with. However, you can see the gap is only widening with time. Time has a role to play.

How Many Apples Can You Buy for Rs 100?

Let’s suppose an apple comes for Rs 10 today. At this price, Rs 100 will fetch you 10 apples. Now, let’s assume price of an apple increases by 8% every year. That means, after 1 year, an apple will cost Rs 11.

YearPrice of an appleHow many apples can you buy for Rs 100?How much do you need to buy 10 apples?
Today10.010.0100.0
111.09.1110.0
212.18.3121.0
313.37.5133.1
414.66.8146.4
516.16.2161.1
617.75.6177.2
719.55.1194.9
821.44.7214.4

You are purchasing the same apples. You still have Rs 100 with you. Just that, over a period of time, the same Rs 100 note can buy you lesser number of apples. In other words, the value of Rs 100 note is going down with time. And that is inflation. Inflation refers to a general increase in prices or loss of purchasing power of money. If you have heard of your parents perennially complaining about how everything is getting expensive all the time, they are essentially talking about inflation. Rs 100 after 8 years does not have the same value as Rs 100 today. In 8 years, you wouldn’t be able to purchase even half the apples you are purchasing today for Rs 100. You need Rs 214.4 to purchase 10 apples after 8 years. Rs 100 today is same as Rs 214.4 after 8 years.

Connecting the Dots

We have considered three different examples in this post. 

  1. The first example about Maruti car was the power of compounding in full flow. 
  2. The second example was a more realistic example of compounding. And we could see how rates of return along with the power of compounding can result in vastly different amount at the end of your investment term.
  3. The third example was to show how your money/currency gradually loses value over a period of time. Inflation will be around irrespective of what you do. In fact, if you see, inflation is also an example of compounding. Just that it works against you. i.e., it is adding to your misery.

Now the question is how do you counter inflation? Frankly, there is nothing you can do to stop inflation. It will be there. However, you can and you must ensure that your money retains it purchasing power. And how do you do that? You can do that by investing your money. Take cues from our second example (doubling the money). If you were to invest your Rs 100 in an investment that gives you 10% p.a. compounded returns, you will have Rs 214.4 at the end of 8 years.

Rs. 100 X (1.10)^8 = Rs 214.4

That is just about the money you need to purchase 10 apples after 8 years. This way, you have been able to keep the purchasing power of your money intact. If you could invest in an investment that gives you 12% p.a. you would have Rs 247 at the end of 8 years. Good enough for you to buy 11.5 apples. In this case, your money has grown faster than inflation and you have been able to beat inflation. 

When it comes to investments, the compounding works in your favour. However, when it comes to inflation, you don’t have a choice. You deal with what you get. In case of investments, you have a choice. You will always have multiple options. For instance, if you had invested at 4% p.a., you would have only Rs 136 at the end of 8 years. You will be able to purchase only 6 apples for that sum. In this case, you have not been able to maintain the purchasing power.

Therefore, if the aim is to counter inflation and maintain the value of your money, you invest your money in places where it is likely to beat inflation.

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