Question

If discount rate is 12%, the present value of Rs X recieved at the end of each year for the next five years is equal to

Answer 1

Present Value =
`X [(1)/((1 + 0.12)^(1) ) + (1)/((1 + 0.12)^(2) ) + (1)/((1 + 0.12)^(3) ) + (1)/((1 + 0.12)^(4) ) + (1)/((1 + 0.12)^(5) ) ]`

Explanation:

To find - If discount rate is 12%, the present value of Rs X received at the end of each year for the next five years is equal to .... ?

Solution -

We know that, formula for finding the Present vale is given by

Present value = Future value / (1 + r)ⁿ

where r is the rate of interest

and n is Number of periods

Now,

Here in the question, we have

r = 12% = 12/100 = 0.12

n = 5

Also, Given that, we have received Rs X at the end of each year

So,

Present Value =
`(X)/((1 + 0.12)^(1) ) + (X)/((1 + 0.12)^(2) ) + (X)/((1 + 0.12)^(3) ) + (X)/((1 + 0.12)^(4) ) + (X)/((1 + 0.12)^(5) )`

=
`X [(1)/((1 + 0.12)^(1) ) + (1)/((1 + 0.12)^(2) ) + (1)/((1 + 0.12)^(3) ) + (1)/((1 + 0.12)^(4) ) + (1)/((1 + 0.12)^(5) ) ]`

⇒Present Value =
`X [(1)/((1 + 0.12)^(1) ) + (1)/((1 + 0.12)^(2) ) + (1)/((1 + 0.12)^(3) ) + (1)/((1 + 0.12)^(4) ) + (1)/((1 + 0.12)^(5) ) ]`