Question

1. (Interest Rate for multiple periods)You have an opportunity to invest $1000 today to acquire an asset which will generate $300 in income two years from today and which can be sold for $900 at that time.

a. Determine the rate of return for this investment. b. What level of the market interest rate would make this investment attractive to you?

2. (Number of Periods) You have decided to save $1000 today hoping it will be worth $2000 someday. Assume you can earn 8.9% rate of return. How long does it take for you to realize this goal?

Answer 1

a)Initial investment = 1000
Income genreated at (t =2) = 300
Price recovery from sales (at t=2) = 900
Rate of Return = (900 + 300 -1000)/1000 = 200/1000 = 20%
the rate at which NPV=0
The interest rate at which it becomes attractive = -1000 + (200+1000)/(1+r)² =0
(1+r)² = 1200/1000
r = (1.2)^0.5 -1 = 0.0954 or 9.544%
At interest rates less than 9.54% project would be attractive.
b)
Amount = Principal * (1+r)ⁿ  
2000 = 1000 * ( 1 + 8.9%)ⁿ
2000/1000 = 1.089ⁿ
Log 2/Log 1.089 = n (applying log to calculate n)
n = 8.129 or 8.13 years

Best of Luck . God Bless