Question

An investment pays you $30,000 at the end of this year, and $15,000 at the end of each of the four following years. What is the present value (PV) of this investment, given that the interest rate is 5% per year

Answer 1

Answer:

Present value of the cashflow discounted at 5% per year 76,815.65

Explanation:

First, we calculate the present value of the 4 years 15,000 dollar annuity:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 15,000.00

time 4

rate 0.05

$15000 \times \frac{1-(1+0.05)^{-4} }{0.05} = PV$

PV $53,189.2576

Now, we discount two more year as lump sum as this is two year after the invesmtent:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  53,189.26

time  2.00

rate  0.05000

$\frac{53189.2575624354}{(1 + 0.05)^{2} } = PV$  

PV   48,244.2245

Finally we also discount the 30,000 by one year

30,000 / 1.05 = 28571.43

We add up both to get the present value:

48,244.22 + 28,571.43 =  76,815.65