The time-value of money means that one dollar today is worth more than one dollar tomorrow. Put diﬀerently, the future value of one dollar is less than the present value of one dollar. ( you can always put this dolar in a banking deposit to earn an interest. )

In the time value of money we try to see how we translate future value of the money in the present and reverse.

**How we calculate the future value of the money?**

For calculationg the future value of the money we use this formula

Also we use the compounding formula, for example for three periods ( the example can be extended for more periods)

Abreviations used :

R0,1 = Rate of Return from Time 0 to Time 1

FV = Future value

PV = Present value

**How much money will you receive in the future if the rate of return is 20% and you invest $100?**

The figure below shows how your $100 would grow if you continued investing it at a rate of return of 20% per annum.

The function is exponential, that is, it grows faster and faster, as interest earns more interest.

When money grows at a rate of 20% per annum, each dollar invested right now will be worth $38.34 in 20 years.

The money at ﬁrst grows about linearly, but as more and more interest accumulates and itself earns more interest, the graph accelerates upward.

And a exercise for those interested in such a subject:

**EX: From Fibonacci’s Liber Abaci, written in the year 1202: “A certain man gave one denaro at interest so that in ﬁve years he must receive double the denari, and in another ﬁve, he must have double two of the denari and thus forever. How many denari from this 1 denaro must he have in 100 years?”**

The next important detail in this subject is about present value, so..

How we translate all futures cash flows into present ?

And right here we can discuss about **Net Present Value – NPV** formula.

In this context, r is called the discount rate or cost of capital, and 1/(1 + r ) is called the discount factor.

The Net Present Value Capital Budgeting Rule states that you should accept projects with a positive NPV and reject projects with a negative NPV.

The translation between future values and present values—and its variant net present value— is the most essential concept in ﬁnance. Cash ﬂows at diﬀerent points in time must ﬁrst be translated into the same units—currency today—before they can be compared or added.

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