Question

Assume you are investing $100,000. You are going to allocate your $100,000 between four securities. Historical average annual rates of return for each security are as follows: Security A: 2%; Security B; 5%; Security C: 9%; Security D:15%.

Round percentage answers to one decimal place. Round dollar answers to the nearest whole dollar.

If you allocate your funds equally between the four securities, what is the average rate of return you will earn? % What will your investment be worth in 15 years, assuming you earn that rate every year? $.

If instead you allocate your funds between the four securities unevenly, using this structure: 10% to Security A, 20% to Securities B and D, and 50% to Security C, what is the average rate of return you will earn? % What will your investment be worth in 15 years, assuming you earn that rate every year? $

Answer 1

Answer :

(i) If Funds are allocated Equally Calculation of Average Rate of Return

Weight of each Fund = 0.25

Average Rate of Return =[ (Return of A * Weight of A) + (Return of B * Weight of B) + (Return of C * Weight of C) + (Return of D * Weight of D)]

Average Rate of Return = (2% * 0.25 ) + (5% * 0.25 ) + (9% * 0.25 ) + (15% * 0.25 )

= 0.5 + 1.25 + 2.25 + 3.75

= 7.75 % or 7.8%

Calculation of value of investment be worth in 15 years, assuming you earn that rate every year

Future Value = Present Value * ( 1 + Average rate of Return ) n

here n = Number of years i.e 15

Future Value = 100000 * ( 1 + 0.075)15

= 100000 * 2.95887735272

= 295,887.735272 or $ 295,888

(ii) If Funds are allocated unevenly

Weight of A = 0.10

Weight of B = 0.20

Weight of C = 0.50

Weight of D = 0.20

Average Rate of Return =[ (Return of A * Weight of A) + (Return of B * Weight of B) + (Return of C * Weight of C) + (Return of D * Weight of D)]

Average Rate of Return = (2% * 0.10 ) + (5% * 0.20 ) + (9% * 0.50 ) + (15% * 0.20 )

= 0.2 + 1 + 4.5 + 3

= 8.7 %

Calculation of value of investment be worth in 15 years, assuming you earn that rate every year

Future Value = Present Value * ( 1 + Average rate of Return ) n

here n = Number of years i.e 15

Future Value = 100000 * ( 1 + 0.087)15

= 100000 * 3.49496765875

= 349,496.765875 or $ 349,497