Time Value of Money

Time Value Of Money

1 Concept

Time value of money shows the relation of value of money with time. Time value of money is also value of interest which we have earned for giving money to other for specific period. Value of Rs. 1 which you have today is more valuable than what Rs. 1 you will receive after one year because you can invest today receive Rs. 1 in any scheme and you can earn minimum interest on it. It means today received money is important than tomorrow receivable money. Interest rate is the cost of borrowing money as a yearly percentage. For investors, interest rate is the rate earned on an investment as a yearly percentage.

Time value of money results from the concept of interest. So it now time to discuss Interest.

1. Simple Interest

It may be defined as Interest that is calculated as a simple percentage of the original principal amount. The formula for calculating simple interest is

SI = P0 (i)(n)

Future value of an account at the end of n period FVn = P0+ SI = P0 + P0(i)(n)

2 Compound Interest

If interest is calculated on original principal amount it is simple interest. When interest is calculated on total of previously earned interest and the original principal it compound interest. Naturally, the amount calculated on the basis of compound interest rate is higher than when calculated with the simple rate.

FV _n = P_o (1+ i) ⁿ

Where,

i =     Annual rate of interest / Number of payment periods per year

= r/k

So, FV _n = P₀ (1 + r/k)ⁿ

When compounding is done k times a year at an annual interest rate r.

Or

FV_n = P_o (i + FVIF) _in

Where,

Effective Rate of Interest

It is the actual equivalent annual rate of interest at which an investment grows in value when interest is credited more often than once a year. If interest is paid m times in a year it can be found by calculating:

Ei = (1+ i/m) ^m -1

3 Present Value

―Present Value‖ is the current value of a ―Future Amount‖. It can also be defined as the amount to be invested today (Present Value) at a given rate over specified period to equal the ―Future Amount‖.

The present value of a sum of money to be received at a future date is determined by discounting the future value at the interest rate that the money could earn over the period. This process is known as Discounting. The present value interest factor declines as the interest rate rises and as the length of time increases.

P_{o =} FV_n /(1+ i) ⁿ

P_{o =} FV_n (1+ i) -ⁿ

Where,

FVn  = Future value n years hence

I        = Rate of interest per annum

n       = Number of years for which discounting is done.

B. Discount (or) present value technique: -

= _{(1+ )}

Present value V_o = Future value (V_n) x DF_in