Calculation of Present Value

Present Value

Before going for the mathematical calculation of present and future values of money, it is desirable to understand the two concepts.

Situation 1: Presume that A lends $1000 to B with the condition that B has to repay the amount after 1 year with interest at 10%. After 1 year, B returns $1100. In this transaction, $1000 with A is the present value of the amount, whose future value is $1100 after one year at 10% interest.

The same situation can also be stated in a reverse way that the present value (P) of a future value (F) of

$1100 at 1 year at 10% interest is $1000.

Situation 2: Suppose that A leases his property to B for two years at an annual lease of $5000 payable on the completion of the first and second years after the start of the lease. But A requires money now itself and requests B to pay the lease in advance. B pays the lease, but only after discounting the lease value for 1 year and 2 years .If the prevailing rate of interest is 10%, B pays A $4500 for first year lease and around $4000 for the second year lease amount. The amounts of $4500 and $4000 are the present values of the amount of $5000 payable after the first and the second years respectively.

Calculation of Present Value

The present value (P) of a sum of money to be received at a future date can be calculated by discounting the future value (F) at the interest rate that the money could earn over the period.

The future value equation is same as the compound interest equation,

                                     

where                                   F = Future value 

                                           P = Present value 
                                            i = Annual interest rate

The present value is given by:

 The term ,

is known as the discount factor.               

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