Question

You are considering investing in a security that will pay you ​$2,000 in 32 years.

a.  If the appropriate discount rate is 10 percent​, what is the present value of this​ investment?

b.  Assume these investments sell for ​$933 in return for which you receive ​$2,000 in 32 years. What is the rate of return investors earn on this investment if they buy it for ​$933​

Answer 1

- Future Value of the Investment to be received in 32 years = $2000

a). Calculating the Present Value of the Investment:-

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

where, r = Periodic Interest rate = 10%

n= no of periods = 32

Present value = $2,000/(1+0.10)^32

= $2,000/21.1137767454

= $94.73

So, the Present value of this Investment is $94.73

b). Present value of the Investment is $933

calculating the rate of return earned on the Investment during period:-

Future value = Present value*(1+r)^n

where, r = Periodic Interest rate

n= no of periods = 32

$2000 = $933*(1+r)^32

2.1436227224 = (1+r)^32

Taking 32-root on both sides,

1.02411 = (1+r)

r = 2.41%

So, the rate of return investors earn on this investment is 2.41%

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