# Time Value of Money

Time value of money is the value of money with the time. Changing purchasing power of money with the exclusion of time. In the period of inflation purchasing power of money is going down day by day. If we invest or deposit some money in the bank, then we receive return or interest on such money. Such return or interest is the compensation for the the loss of value of money for such length of period. It is true that money received today is more valuable than money received in future. It is vice versa in the environment of deflation. Thus changing value of money with the period of time in both the environment is known as Time value of money.

There are two types of TVM: –  1. Present value of money
2. Future value of money

Present value is the value today of an amount that is receivable in future with the investment rate for the period of time. The investment rate is known as discounting rate discounting factor, hurdle rate etc.
It is calculated by the technique of discounting.
Future value is the compounded amount of money after a period of time with the interest rate. It is calculated by the technique of compounding.

Difference between simple and compound interest:-
Simple interest is due periodically and paid periodically. It is not accumulated with the principal amount.
Compound interest is due periodically but not paid regularly and periodically. It is accumulated with the principal.
SI = Pit
A= P + Si
A= P+Pit
= P (1+it)
Compound Amount= P (1+i) n
A is future value
P is present value
For finding out present value:-
P= A/ (1+i) n
P= future value * 1/ (1+i) n
P= FV * present value of re 1 @ i % due after n years
In calculator
Assume i = 10%, n= 3 yr
Then (1+i) = 1.1
1.1    ÷   = for first year
=       for second year
=       for third year
If the value is repeated, it means it’s an annuity… then press m+ after every = sign
And at last press MRC.
Difference between Annuity and Perpetuity:-
Both are paid annually and regularly but the main difference is time period.
Annuity is paid for a period of time, but perpetuity is paid forever.
Annuity has an end life, perpetuity has no end.
Present value of an annuity:-
Present value of multi period perpetuity:-
=  C
r

C= compounded value of perpetuity
r = rate of interest per payment period
Present value of growing perpetuity:-
=   C
r-g
Where g= growing rate
That’s all about the time value of money.