Question

Rearrange the future value equation to show the present value (include explanations for each step).

Answer 1

Future value of a single sum=Its Present value *(1+Interest rate)^No.of compounding periods

Stating in short form,

FV=PV*(1+r)^n

where FV=Future value at the end of n compounding periods

at the rate of r% per compounding period.

n=no.of compounding periods

It is the same as thevery basic principal,compund interest ,no.of periods & amount formula, we have learnt in middle-grades in schools.

A=P*(1+i)^n

Here, A= the amount or the Future value of the Principal or the initial amount

P= the Principal or the initial amount

i= interest rate per period

n= No.of periods

A=FV;P=PV;i=r & n=n

So,

FV=PV*(1+r)^n

OR

PV*(1+r)^n=FV

Now, to leave PV alone on the left side of the equation,

we need to divide the left-hand side by (1+r)^n

so we divide the right-hand side also by (1+r)^n--so as not to affect the equation mathematically.

ie.PV*(1+r)^n/(1+r)^n=FV/(1+r)^n

Simplifying both sides,we get

PV=FV/(1+r)^n

So, PV stated in terms of FV=

PV=FV/(1+r)^n