An investor has $12,000 to invest into two different funds. Fund A, which is a high risk fund, yields an average return of 14%. Fund B, which is a low risk fund, yields an average return of 6%. To reduce the risk, the investor wants the amount in fund B to be at least twice the amount in fund A. How much should be invested in each fund to maximize the return?

Question

Mathematics

Pierre Tate

8 August, 07:04

An investor has $12,000 to invest into two different funds. Fund A, which is a high risk fund, yields an average return of 14%. Fund B, which is a low risk fund, yields an average return of 6%. To reduce the risk, the investor wants the amount in fund B to be at least twice the amount in fund A. How much should be invested in each fund to maximize the return?

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Mckee · Answer 1

The problem gives a principal of $12,000 that is divided into two funds with different average of return. To solve the appropriate amount for each fund. We must first get the years in which two funds are invested. The equation is 1.14^x = 2*1.06^x where x is the number of years. 2 means fund in B must be twice that in A as given. x is equal to 9.53 years. We substitute x to find y in

y (1.14) ^9.53 = (12,000-y) * 1.06^9.53 where y is the fund in A. y is equal to 4,000. So in Fund A, $4000 is given while in Fund B, $8000 is invested.