Hello, josh123!
A fascinating problem . . .
Past history indicates that mutual fund A will earn 14.6% annually while mutual fund B will earn 9.8% annually.
If an investment amount is divided between funds A and B so that the expected return will be 11%,
how should the investment be split between the two funds?
a. 1/4 to A; 3/4 to B
b. 1/5 to A; 4/5 to B
c. 1/6 to A; 5/6 to B
d. 2/3 to A; 1/3 to B
e. 1/3 to A; 2/3 to B
f. none of these
Let \(\displaystyle A\) = amount invested in fund A.
Let \(\displaystyle B\) = amount invested in fun B.
The \(\displaystyle A\) dollars invested in fund A earns 14.6%.
. . The earnings are: \(\displaystyle 0.146A\) dollars.
The \(\displaystyle B\) dollars invested in fun B earns 9.8%.
. . The earnings are: \(\displaystyle 0.098B\) dollars.
Hence, the total earnings is: \(\displaystyle 0.146A\,+\,0.098B\) dollars.
But we are told the the earnings of the total investment is 11%.
. . That is, the earnings are: \(\displaystyle 0.11(A\,+\,B)\) dollars.
And
there is our equation:
. \(\displaystyle 0.146A\,+\,0.098B\:=\:0.11(A\,+\,B)\)
. . and we have:
.\(\displaystyle 0.146A\,+\,0.098B\:=\:0.11A\,+\,0.11B\)
. . which simplifies to:
.\(\displaystyle 3A\,=\,B\;\;\Rightarrow\;\;\L\frac{A}{B}\,=\,\frac{1}{3}\)
The ratio of \(\displaystyle A\) to \(\displaystyle B\) is 1 to 3.
Therefore:
.\(\displaystyle \frac{1}{4}\) to A;
.\(\displaystyle \frac{3}{4}\) to B . . . answer choice (a)
