Question

A person plans to invest twice as much in a.) Putnam Global Equity fund at 11.9% annual interest as in b.) Bridgeway Small Cap at 20% annual interest. How much will the person have to invest in each fund to earn a total of $2800 in one year?

Answer 1

He has to invest $9,169 in Putnam Global Equity and $4,584.5 in Bridgeway small cap to earn a total of $2,800 in interest for one year

Here, we want to find how much has to be invested in each fund

From the question, the investment in a is twice that of b

So, if he invests $x in b, he would be investing $2x in a

Let us work with the interests now

In the case of the interests, the total amount of interest in both will equal $2800 per year

Thus, we have that;

`\begin{gathered} 11.9\text{ percent of 2x + 20 percent of x = 2,800} \\ \\ (11.9)/(100)\text{ }*\text{ 2x + }(20)/(100)* x\text{ = 2,800} \end{gathered}`

Multiply through by 100;

`\begin{gathered} 2x(11.9)\text{ + 20(x) = 100(2,800)} \\ 23.8x\text{ + 20x = 200,800} \\ 43.8x\text{ = 200,800} \\ x\text{ = }(200,800)/(43.8) \\ x\text{ = 4584.5} \end{gathered}`

To get the investment in a, we simply multiply this result by 2 and we have 2(4584.5) = $9,169