# Time Value of Money

Time value of money implies that rupees paid or received in the future are different from the rupees paid or received today.

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:

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).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:

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.

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.

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

**Important Points to Remember:**

**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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