- The future value of a single cash flow implies that how much will be worth of money after a few years if it is invested today at a prevalent rate of interest. E.g.: What will be the return on the maturity of a bank FD of Rs 10000 done today at a fixed rate of interest for 2 years.

### Calculation of Future Value

**Aman has invested Rs 50000 in Fixed Deposit for 3 years, with an expected return of 10% per year, he wants to know the maturity value or the future value of his investment after 3 years?**

__Example 1:__- The problem statement above is a very common doubt, almost everyone who wants to invest has this question in mind that what will be the Future Value of my Current Investment.

- Lets us see how it is calculated,
- To Answer to the above question, we have a formula:
**FV = PV (1+R)**^{T}- Where FV is the Future Value we want to calculate
- P is the Principal Invested
- R is the Expected Rate of return
- T is the time for which investment is done
- Substituting the values in the formula,
**FV = 50000 (1 + 0.1)**^{3}= 100000 (1.1)^{3}= Rs 66550.00- The Formula above is the same as Formula for Calculation of compound Interest and it can be easily used to find Future Value of a sum invested today at a certain rate of interest.

**What will be Future Value of Rs 25000 invested after 10 years, if the Rate of Interest is 10% PA, then what will be the future value of the investment after 20 years**

__Example 2:__- Solution: As we know, FV =
**PV (1+R)**^{T} - PV = 25000, R= 10%, T= 10 years (20-10 years, as the amount, will be invested for net 10 years only)
**Hence, FV = 25000 (1 + 0.1)**^{10}= Rs 64843.56

###
**Power of Compounding**

- Given below is the demonstration of the power of interest/compounding over various periods. Future Value of Rs 10000 at 5% interest rate for a various number of years is calculated, it is interesting to note that the growth is not proportional, rather it seems more like exponential, this is known
**as the power of compounding.**

## Additional Point

**Rule of 72:**This is a simple rule to find out that if the rate of interest is x%, then in how many years the invested amount will double itself.- The rule says that the amount invested will get doubled in
**72/x years.**

**If the rate of interest is 12% PA, then in how much time will an investment double itself?**

__Example 3:__**Solution:****Using the Rule of 72,**the invested amount will double itself in**72/12 i.e. 6 years**

**Calculate the rate at which Rs 20000 invested today will yield a maturity of Rs 24200 in 2 years.**

__Example 4:__**Solution:**As given, PV = Rs 20000, FV= Rs 24200, T=2 years, R=?**We know that, FV = PV (1+R)**^{T}- Substituting the values, 24200 = 20000
**(1+R)**^{2}**= 24200/20000 =****(1+R)**^{2} - This becomes, 1.21 =
**(1+R)**, as we know 121 is square of 11, so 1+R = 1.1^{2} **Hence Rate = 0.1 or 10%**