Precalculus: find yield on taxable fund to match return

[absolutjosh]

An investor had a choice of two investments: a bond fund and a stock fund. The bond fund yeilds 7.186% interest annually, which is nontaxable at both the federal and state levels. Suppose the investor pays federal income tax at a rate of 28% and state income tex at a rate of 7%. Determine what the annual yield must be on the taxable stock fund so that the two funds pay the same amount of net interest income to the investor.

 

[Deleted member 4993]

An investor had a choice of two investments: a bond fund and a stock fund. The bond fund yeilds 7.186% interest annually, which is nontaxable at both the federal and state levels. Suppose the investor pays federal income tax at a rate of 28% and state income tex at a rate of 7%. Determine what the annual yield must be on the taxable stock fund so that the two funds pay the same amount of net interest income to the investor.

What does your textbook say - What your thoughts - Where exactly are you stuck?

For starter - if the investor does not to invest equally in those two funds (and your problem does not say so) - then it can be anything.

 

[stapel]

Since you're dealing with percentages, you can pick any arbitrary starting value. So suppose your amount to invest is, say, $1000.

You are told how much the bond fund yields, so find the interest on that investment.

You now have the value you need to match. (I will assume that the stock fund is taxed only on the income, not on the initial $1000.) At the end of the year, you will have your initial investment amount, plus whatever return is left after the 35% total taxes. That is, you'll have your $1000, plus 65% of your return:

. . . . .$1000 + (65%)[(some rate of return)($1000)]

Simplifying, we get:

. . . . .$1000[1 + (65%)(some rate of return)]

Convert the percentage to a decimal, pick a variable to stand for the unknown, set the expression equal to the desired value (found above), and solve for the variable.

Hope that helps!

Eliz.

P.S. Welcome to FreeMathHelp!

 

[Denis]

x = yield on stock fund

x - .35x = .07186 ; solve for x