Word Problem/Finance/Investments and tax brackets

[jameswingle]

Two possible investments are munciple bonds and treasury bonds.

Interest earned on a munciple bond is free of both federal and state taxes, whereas a treasury bond is only free of state taxes. However, treasury bonds usually pay higher interest rates. Deciding on the better choice depends not only on the interest rates, but also on your fedeeral tax bracket. (also known as the marginal tax bracket, is the perrcent of tax paid on the last dollar earned). If t is the tax free rate and x is your tax bracket (as a decimal), then the formula:

r=t/(1-x) gives the taxable rate r that is equivalent to a given tax free rate.

1. Suppose a one year municipal bond pays 4% interest. Graph the function defined by r(x)=.04/(1-x) for 0 is less than x and x is less than or equal to .5. If you graph by hand use the x values .1,.2,.3,.4, and .5. If you use a graphing caculator, use the viewing window [0,5] by [0,.08]. Is this a linear function? Why or why not?

I tried doing this by hand substituting the values given by x, but what is y? I got .04,.05,.06,.07,.08..respectively. On the calculator I set y = to all values that I got and of course I got a straight horizontal line. What am I doing wrong?

2. What is the equivalent rate for a one year treasury bond if your tax bracket is 31%?

I tried to set r=t/1-.36, which gave me .69, but I do not know how to find t

3. If a 1 year treasury bond pays 6.26%, in how high a tax bracket must you be before the municipal bond is more attractive?

I didn't have a clue how to set this up

Thanks in advance for your help, word problems have always been a problem for me. You guys are life savers, thanks again!

 

[stapel]

I tried doing this by hand substituting the values given by x, but what is y?

The output is exactly what the exercise states: "the taxable rate r that is equivalent to a given tax-free rate."

On the calculator I set y = to all values that I got and of course I got a straight horizontal line. What am I doing wrong?

Since "y = (a number)" is a horizontal line, the calculator has graphed your inputs correctly. But what are you trying to do here? Why not plug the given input formula into your calculator? :?:

I tried to set r=t/1-.36, which gave me .69, but I do not know how to find t

You might want to re-read the exercise, and look at the formula you were given for part (2), which should make fairly obvious the value you should use for "t" in this instance. :wink:

3. If a 1 year treasury bond pays 6.26%, in how high a tax bracket must you be before the municipal bond is more attractive?

I didn't have a clue how to set this up

You are given the value of t, and asked to find the value of x so that r is greater than the stated bond interest rate. So plug in the given values, and solve for the value of x. :idea:

Eliz.

 

[jameswingle]

I am still having problems with this. I don't understand in problem 1 why the interest was plugged into the value of t which I thought was =to the tax free rate. Also, the way the problem is written r(x)=t/(1-x). Does this mean that it is a function of x? I used my calculator as y=.04/(1-x) and got a graph, but how do I prrove it is a linear graph? If I can figure out #1 then 2 won't be a problem, but # 3 still has me stumped. Any further advice?


Thanks

 

[stapel]

I used my calculator as y=.04/(1-x) and got a graph, but how do I prrove it is a linear graph?

Um... it isn't linear! :shock:

Eliz.

 

[jameswingle]

Sorry, I meant not linear the line has a curve that goes to positive infinity. However, how can I prove that the graph is not = to f(x) = ax+b. Also, did i input it right? Finally,for #1 i got 0.0775; 2: 0.0276, and 3: 0.0446. am I on the right track. I really not that stupid, but this is an online course and my computer crashed the day before it started, so on this chapter I have been rushing it trying to catch up. Thanks for your time, I know your busy.