You need to decide how to invest a graduation gift of $1000. The annual rate of return is given in the next table for each of three different types of investments and three different states of the economy.

Recession Stable Economy Expansion

 Investment A 2.5% 2.5% 2.5%

 Investment B 2% 4% 5%

 Investment C -2% 4% 10%

a. Create a table that gives the amount of money for each type of account and state of the economy after one year, if interest is compounded monthly.

b. Compute the expected value of your account at the end of one year for each of the investment types, if the probability of a recession is 0.5 and the probability of a stable economy is 0.3.

Solution:

(a)

Recession Stable Economy Expansion

 Investment A 1025.29 1025.29 1025.29

 Investment B 1020.18 1040.74 1051.16

 Investment C 980.18  1040.74  1104.71

(b)

 Investment A: E(x)=0.5*1025.29+0.3*1025.29+0.2*1025.29 = 1025.29

 Investment B: E(x)=0.5*1020.18+0.3*1040.74+0.2*1051.16 = 1032.54

 Investment C: E(x)=0.5*980.18+0.3*1040.74+0.2*1104.71 = 1023.35