Respuesta :
Answer:
Present Value = [tex]X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ][/tex]
Step-by-step 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 = [tex]\frac{X}{(1 + 0.12)^{1} } + \frac{X}{(1 + 0.12)^{2} } + \frac{X}{(1 + 0.12)^{3} } + \frac{X}{(1 + 0.12)^{4} } + \frac{X}{(1 + 0.12)^{5} }[/tex]
= [tex]X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ][/tex]
⇒Present Value = [tex]X [\frac{1}{(1 + 0.12)^{1} } + \frac{1}{(1 + 0.12)^{2} } + \frac{1}{(1 + 0.12)^{3} } + \frac{1}{(1 + 0.12)^{4} } + \frac{1}{(1 + 0.12)^{5} } ][/tex]
