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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 â‚¹1000 in your wallet today is worth more than â‚¹1000 in your wallet 5 years in the future. This is because you can invest that â‚¹1000 in your savings account and earn interest for 5 years and get more than â‚¹1000 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 â‚¹1000 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 â‚¹1000 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 â€“ 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 â‚¹1000 (=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 â€“ in this each yearâ€™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 â‚¹16.6576 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 â‚¹1000 would give you a total of â‚¹3,800 (1000 principal and 2800 as interest). With compounding, you would get â‚¹14,785 (1000 principal and 13785 as interest). A 5x difference.

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.

Eg 1: if you put â‚¹10,000 per year @ 8% interest rate compounded yearly for 35 years, how much would you get? Ans. â‚¹ 18,61,021.

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

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

Last modified 7mo ago

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