**Time Value of Money Essay, future value of a sum, present value of a sum and annuity. What is the importance of money in life essay samples.**

## Definition of The Time Value of Money

Time value of money is an accounting concept that values the current worth of a dollar more than its future equivalent. As such, time value of money states that the value of a unit dollar to be received at a future date is less than the value of a similar unit at hand today (Bianco, Nelson, and Poole, 2010).

### Short Paragraph on Money

Preference of money at current date is influenced by the fact that money to be received at a future date is subjected to various factors such as inflation, default risk and interest rate fluctuations. There are four concepts under the time value of money:

## Future Value of a Sum (FV)

The future value of a sum of money is defined as the amount of money that an individual will obtain at a future date if the present sum is invested for the period up to that future date at a given interest rate.

Therefore, the future value of a single sum is the sum of the present value of that amount and the compound interest that will accrue for the period until that future date. The future value of a sum is computed using the following formula:

Future Value (FV) = Present Value (PV) × (1 + i)^{n}

From the formula, I is the rate of interest per compounding period, and n is the number of periods.

For instance, an amount of $20,000 invested of January 1, 2010 at an interest rate of 8% compounded annually.

The future value of the investment on Dec 31, 2013, given quarterly compounding will be given as follows.

PV = $20,000

n = 4 × 4 = 16

i = 8% /4 = 2%. Therefore, future value will be

FV = $20,000 (1 + 2%)^{16}

= $20,000 * 1.3727851

= $27,455.71

The future value of a sum is used to compute the amount of money that an investor will attain at a given future date when invested now as a lump sum, considering the time value of money (Bianco, Nelson, and Poole, 2010).

## Present value of a sum

The present value of a sum of money is the amount that equates the sum invested and the compound interest earned on the investment with the face value, if invested at a specific rate of interest on a given date (Damodaran, 2010).

It is the sum obtained after discounting the future value at a given rate of interest. The present value of a future sum is calculated using the following formula:

Present Value (PV) = | Future Value (FV) |

(1 + i)^{n} |

For instance, given a future value of $27,455 to be received on December 31, 2013 at an interest rate of 8% compounded quarterly, we can find the present value as follows:

FV = $27,455

n = 16

i = 2%

PV = $27,455 / (1.02)^{16}

= 27,455 / 1.3727851

= $20,000

Present value computations assist business organizations when making capital budgeting decisions. It indicates whether making an investment produces positive present value on returns.

## Present Value of an Annuity

An annuity is a series of equal payments that are evenly made after specific periods of time. Therefore, the present value of an annuity is the total sum of all periodic payments discounted at a certain rate of interest to reflect the time value of money (Damodaran, 2010).

It is the amount that will equate the sum invested and compound interest earned with the face value of each payment and the product of the number of periodic payments.

The present value of an ordinary annuity is calculated using the following formula:

Present Value of an Ordinary Annuity = R × | 1 − (1 + i)^{-n} |

i |

Where R is the fixed periodic payment; i the interest rate per compounding period; and n =the number of compounding periods.

For example, the present value of an annuity of $500 payments made at the end of each month for the year 2011, at an annual interest rate of 12% will be calculated as follows:

R = $500

n = 12

i = 12% / 12 = 1%

PVA = $500 * (1 – (1.01^{-12}) / 1%

= 500 * 0.11255/0.01

= 500 * 11.255

= $5,627.54.

The present value of the annuity concept helps business lenders determine whether it is viable to advance their funds to debtors.

## Future Value of Annuity

The future value of an annuity is the sum of face value, periodic payments and the total interest earned compounded on all the periodic payments up to the future value point (Damodaran, 2010). It is the value of periodic payments enhanced at a certain rate of interest for each period to reflect the time value of money.

Future value of an ordinary annuity of a sum is calculated using the following formula:

Future Value of Ordinary Annuity = R × | (1 + i)^{n} − 1 |

i |

Future value of an annuity is used by investors to determine the total value of their periodic investments at a future date, such as pension or insurance contributions.

## Importance of the Time Value of Money Concept

Time value of money is often used in financial decision making models to maximize the economic welfare of shareholders (Tirole, 2009). As such, the concept is used in investment decision making and financing decisions.

Investment decision involves optimal allocation of capital for long-term investment projects. Since future cash flows from a given project are not equal, investors often discount them into present value for ease of comparison.

### Importance of Money in Life

As such, the returns on investment of a project can be used to appraise its viability. Time value of money is also used by investors in securities such as stocks and bonds (Bianco, Nelson, and Poole, 2010).

In financing decisions, managers use the time value of money concept to design an optimal capital structure and getting finances from sources with the least cost of financing. Different sources of financing can also be compared with this concept to determine the best alternative that has the minimal cost possible and maximum benefit.

### Bibliography on Value of Money Essay

- Bianco, C.A., Nelson, D.T. & Poole, B.S. 2010, “Teaching Time Value of Money”,
*The Business Review, Cambridge,*16, no. 1, pp. 25-31. - Damodaran, A. 2010,
*Applied corporate finance*. Wiley. - Tirole, J. 2009,
*The theory of corporate finance*. Princeton University Press.