What is the relation between the present value factor and the future v

QUESTION

What is the relation between the present value factor and the future value factor?

Present value is the current worth of a sum of money received at a future date. Dollar 1 today is not same as Dollar 1 received after a year. This change in the worth of money is due to the concept of the time value of money. To calculate present value, a technique called discounting is used. Using discounting, PV = FV/(1 r)^t; where FV is the Future Value, PV is the Present Value, r is the interest rate per compounding period and t is the number of compounding periods. 1/(1 r)^t is called the present value factor which can be multiplied with the future values to obtain the present values.Future value is the worth of a sum of money at a future date. To calculate future value, a technique called compounding is used. Using compounding, FV = PV*(1 r)^t. (1 r)^t is called the compounding factor, which is multiplied¦

h the present values to calculate the required future values. Present value and future value factors are available in tables which can be used directly to save the time of calculating manually. Clearly, future value and present value factors are reciprocal of each other i.e. PV factor = 1/ FV factor. However, for an annuity this relationship doesnt hold true. FV= A((1 r)^t-1)/r for an annuity thus the FV factor is ((1 r)^t-1)/r and PV = A*[(1-(1 r)^-t)/r], thus the PV factor is [(1-(1 r)^-t)/r]; where A is the annuity amount.

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