QuestionYou have \ $3200 to invest in three funds with returns of$ 10\% $,$ 7\% $, and$ 5\%$. Invest twice as much in growth as in money market. How to allocate?

Studdy Solution

STEP 1

Assumptions1. The total amount to invest is $3200. The percent return rates for the growth fund, income fund, and money market are10%,7%, and5% respectively3. The amount to be invested in the growth fund is twice the amount to be invested in the money market4. The total investment is distributed among the three funds

STEP 2

Let's denote the amount of money to be invested in the money market as $x$ . According to the problem, the amount to be invested in the growth fund is twice as much as in the money market, so we denote it as $2x$ . The remaining amount will be invested in the income fund, so we denote it as $3200 -x$ .

STEP 3

Write down the equation that represents the total amount to be invested.
$x +2x + (3200 -3x) =3200$

STEP 4

implify the equation.
$4x =3200$

STEP 5

olve the equation for $x$ .
$x =3200 /4 =800$

STEP 6

Now that we have the value for $x$ , we can find the amount to be invested in the growth fund and income fund.The amount to be invested in the growth fund is $2x$ .
$Growth\, fund\, investment =2x =2 \\times800 =1600$ The remaining amount will be invested in the income fund, which is $3200 -3x$ .
$Income\, fund\, investment =3200 -3x =3200 -3 \\times800 =800$ So, the distribution of the $3200 investment across the three funds is$ 800 in the money market, $1600 in the growth fund, and$ 800 in the income fund.

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