# Time Value of Money

This is one of the most important concepts in finance. It implies that rupees paid or received *in the future* are different from the rupees paid or received *today.* It is easier to understand that ₹1000 in your wallet today is worth more than ₹1000 in your wallet 5 years in the future. This is because you can invest that ₹1000 in your savings account and earn interest for 5 years and get more than ₹1000 5 years later.

There are 2 types of calculations which answer 2 different questions:

1. What will be the value of an investment (or a series of investments) after a certain period of time? This question asks about the *Future Value.* Basically how much will be the *Future* value of the investment. Eg. You have ₹1000 rupees today, so the Future Value will give you the value of 1000 rupees after a certain amount of time (=future).
2. What will be the investment (or a series of investments) needed today (present) which would provide a target amount at a future date? This question asks for the *Present Value.* Eg, if I want ₹1000 after 5 years, what would be the amount (called Present Value) which I would need to put in today.

Two types of Interest Calculations:

1. Simple Interest – SI = P x R x T, where P= principal, R= rate of interest and T= time in years. So, if the bank account gives you 4% (=R) and you put ₹1000 (=P) for 5 years (=T), the interest would be (1000) x (4/100) x (5) = 200. And you will get 1000 (the principal) and 200 (the interest) after 5 years = 1200.
2. Compound Interest – in this each year’s interest also starts to get interest like the principal (if compounding is yearly).

| Year | Principal | Rate of Interest | Interest at Year End | Total Value at Year end |
| :--: | :-------: | :--------------: | :------------------: | :---------------------: |
|   1  |    1000   |         4        |          40          |           1040          |
|   2  |    1040   |         4        |         41.6         |          1081.6         |
|   3  |   1081.6  |         4        |        43.264        |         1124.86         |
|   4  |  1124.86  |         4        |         44.99        |         1169.86         |
|   5  |  1169.86  |         4        |         46.79        |         1216.65         |

Due to the effect of compounding, one would get ₹16.6576 more than what one would have got with simple interest. This looks small, but compounding has great effects over long periods of time.

Eg. For a period of 35 years, an 8% simple interest on ₹1000 would give you a total of ₹3,800 (1000 principal and 2800 as interest). With compounding, you would get ₹14,785 (1000 principal and 13785 as interest). A 5x difference.

**Future Value of a Single Investment**

FV = (Present Value of Money) x (1 + Rate of Interest) ^ (number of years). For our example of 1000 kept at 4% for 5 years, the calculation would be: FV = (1000) x (1 + 0.04)^(5) Or, FV = (1000) x (1.04)(1.04)(1.04)(1.04)(1.04) Or, FV = 1216.

**Future Value of a Constant Series of Investments** The excel formula of FV is there for this calculation. [A decent web Link](http://www.calculatorsoup.com/calculators/financial/future-value-annuity-calculator.php).

Eg 1: if you put ₹10,000 per year @ 8% interest rate compounded yearly for 35 years, how much would you get? Ans. ₹ 18,61,021.

**Present Value of a Single Amount** If you want to have ₹1000 after 5 years, how much money do you need to put aside today if you can earn 4%. This is the reverse of the calculation of FV. PV = FV *divided by* (1 + interest rate) ^ (number of years) PV = 1000 / (1+0.04)^5 = 821. This means that the value of ₹ 821 today is the same as ₹ 1000 after 5 years, if we can earn a 4% return on our money.

**Present Value of a Series of Investments**

The excel function PV would be helpful in this. A [weblink](http://www.calculatorsoup.com/calculators/financial/present-value-annuity-calculator.php)

## **Important Points to Remember:**

• The value of money changes with time because it can be invested and earn an interest.

• The longer the time frame, greater would be the difference between the present value and the future value.


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