Future Value of a single sum of money is linked with the Time Value of Money. It is one of the important features of Finance. The Time Value of Money works on the basis that the present value of the money in hand is having more worth than the worth it will be having in future. This is because of its potential earning capacity. The time value of money in short says that the value of money is more today than in future. Therefore, it prefers that receive the money now rather than future. Thus it gives preference to time. It explains the fact that why interest is received or paid. It is just to compensate for the time for which the amount is kept by us or kept by another person. Thus it is important to account for the value of amount in single as well as future.

For example, in case of a savings bank account, the amount is deposited in the bank account and withdrawn at a later period. The depositor receives a simple interest or compounded interest on the deposit made. This interest so received is for compensating the time value for which the amount is kept by the bank.

Basic terms that need to be understood for the Time Value of Money Concept:

**Present Value**: The present value is the current value of future amount of cash flows at a given specified rate of return.**Present Value of Annuity**: Annuity is a continuous receipt or payment that occur at a specified equal interval of time.**Present Value of Perpetuity**: Perpetuity is the infinite and constant flow of identical cash flows.**Future Value**: Future value if the value of the asset in the future, on a specified date based on the amount invested today.**Future Value of an Annuity**: It is the future value of the series of payments at a given rate of interest.

The basic notations used for understanding the time value of money.

- PV is the current value of cash flows (present value)
- FV is the future value of the cash flows after a period n (future value)
- A is the value of payments for each compounding year.
- n is the number of years or periods.
- i is the interest rate at which the amount compounds each period
- g is the growing rate of payments over each time period

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The formulae can be understood as follows:

- Future Value of a Present Sum: FV = PV .(1 + i)
^{n} - Present Value of a Future Sum: PV = FV/(1 + i)
^{n}

In case of Cumulative present value of future cash flows: - Present Value of an annuity for n payment periods:
- Present Value of a Perpetuity: PV(P) = A/i
- Future Value of a growing annuity:

Where i ≠ g,

Where i = g

FV(A) = A.n (1 + i )^{(n-1)} - Future Value of an annuity:

Thus we see how we can calculate different values from different given present values or future values. This study is widely used to make the estimates. The basic thing is doing these studies is the use of proper discounting factors or the rate of returns. Ig the rate of returns or the discounting factors so used are wrong, it will render the whole calculation wrong and thus it will be of no use for the business. It will give wrong results and estimates. The business is run up on the future forecasts only. If it becomes wrong the whole process will be falsified. Thus it is to be taken care of while setting the estimates for the rate of discounting factor or the rate of returns.

**Capital budgeting**: Time value of money helps in ascertaining the value of the capital budgeting techniques and helps to evaluate the best suited plan for the business. It takes into consideration all the aspects of the transaction, evaluates them compares them with other factors and finally take the decision for the best suited plan.**Time Value**: The concept of future value of a single sum helps to ascertain the value of the time and the value of the investment in the future. It is very important to ascertain the value so as to take the decision which is helpful for the business. Thus the time value of money helps in ascertaining the best possible investment. If this decision is taken carefully, it will yield the business a lot of profits.**Convert Value**: The future value of a single amount is a method which helps in determining the value of the investment in future so as to assist the planning process. This method enables the management to forecast the future and make plans as to where to invest and how much to invest. This is very helpful in the capital budgeting process.

Thus we see how important the future value of a single amount has become.

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Where,

Amount is the money deposited today

I/Y is the rate of return per compounding period

n is the total number of compounding periods

How much will an investor have if he deposits $1000 in a account which pays 9% interest after 10 years?

By the help of formula we have,

Future value = 1000(1.09)^{10}

= 1000*2.3673

= $2367.3

Thus, after 10 years $1000 will become $2367.3, here the interest part is 2367.3-1000 = 1367.3. Out of this interest part the part attributable to compounding factor is 1367.3-900 = $467.3

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