Question

What is the present value of a security that will pay $50,000 in 20 years if securities of equal risk pay 5% annu Round your answer to the nearest cent.

Answer 1

Solution :

The present value of a security payment, received at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

PV = Present Value   ; C_n : Cash Inflow at period n ;

r = discount rate ; n = Number of periods or years

As per the information given in the question we have

r = 5 % ; n = 20 years

C₂₀ = $ 50,000

Applying the above values in the formula we have

PV = $ 50,000 / ( 1 + 0.05 ) ²⁰

= $ 50,000 / ( 1.05 ) ²⁰

= $ 50,000 / 2.65329771

= $ 18,844.4741

= $ 18,844.47 ( when rounded off to the nearest cent )

Thus, the Present value of a security that will pay $ 50,000 in 20 years when the discount rate is 5 percent is

= $ 18,844.47

Note : The value of ( 1.05 ) ²⁰   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.05,20) = 2.65329771