When making future plans we would often like to known how much money we must invest now to receive a certain desired amount S at some later date. In other words, we are asking for the original invested principal, which is called the present value or capital value of the amount. Thus if money  is worth I per period, the present value of S due in n periods is that principal which, invested now at the rate i per period, will amount to S in n periods.

Formula for present value

To obtain a formula for the present value, we solve the compound amount formula S = P (1+ i)ⁿ for P by dividing both sides by (1+i)ⁿ. This gives P = S (1+i)^-n.

Thus the present value of s due periods hence at the rate I per period is given by

P = S (1 + i)^-n

The quantity (1 + i)^-n in the above formula is called the discount factor. It represents the present value of Rs. 1 due n periods hence at the rate i per period. Values of (1+ i)^-n for various n and i are given in.

Note. It should be noted that P and S represent the value of the same obligation at different dates. P is the the present value of a given obligation,

while S is the future value of the same obligation. P is just as good as S (N periods hence).

To obtain a formula for the present value in the case of continuous compounding. we solve the equation S = Pert for P. This gives P = Se ^-rt

Thus the present value of s due at the end of i years at the annual rate of r compounded continuously is given by

P = Se ^-rt

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