Mixing
Minimum Rate of Return
$begingroup$
Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the payment of taxes, must the investment offer to be justified?
This is a question under "Simple Interest" from the book I am using. The formulas I know in that topic is:
Simple Interest = (Principal Cost)(rate of interest)(number of periods)
Simple Interest = Future amount - Principal amount. Where in F = P (1 + in)
Rate of Return = [(Current value - Original Value) / (Original Value)] x 100
But I can't relate any of those formula for the problem above. The book shows no solution, just the correct answer: 12.07& Tried to search online for the solutions but no luck.
Just a clue would suffice on how to answer the problem. Any help would be appreciated. Thank you.
finance economics
asked Feb 1 at 15:16
JayceJayce
180111
$endgroup$
add a comment |
$begingroup$
Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the payment of taxes, must the investment offer to be justified?
This is a question under "Simple Interest" from the book I am using. The formulas I know in that topic is:
Simple Interest = (Principal Cost)(rate of interest)(number of periods)
Simple Interest = Future amount - Principal amount. Where in F = P (1 + in)
Rate of Return = [(Current value - Original Value) / (Original Value)] x 100
But I can't relate any of those formula for the problem above. The book shows no solution, just the correct answer: 12.07& Tried to search online for the solutions but no luck.
Just a clue would suffice on how to answer the problem. Any help would be appreciated. Thank you.
finance economics
asked Feb 1 at 15:16
JayceJayce
180111
$endgroup$
2
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49
add a comment |
$begingroup$
Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the payment of taxes, must the investment offer to be justified?
This is a question under "Simple Interest" from the book I am using. The formulas I know in that topic is:
Simple Interest = (Principal Cost)(rate of interest)(number of periods)
Simple Interest = Future amount - Principal amount. Where in F = P (1 + in)
Rate of Return = [(Current value - Original Value) / (Original Value)] x 100
But I can't relate any of those formula for the problem above. The book shows no solution, just the correct answer: 12.07& Tried to search online for the solutions but no luck.
Just a clue would suffice on how to answer the problem. Any help would be appreciated. Thank you.
finance economics
asked Feb 1 at 15:16
JayceJayce
180111
$endgroup$
Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the payment of taxes, must the investment offer to be justified?
This is a question under "Simple Interest" from the book I am using. The formulas I know in that topic is:
Simple Interest = (Principal Cost)(rate of interest)(number of periods)
Simple Interest = Future amount - Principal amount. Where in F = P (1 + in)
Rate of Return = [(Current value - Original Value) / (Original Value)] x 100
But I can't relate any of those formula for the problem above. The book shows no solution, just the correct answer: 12.07& Tried to search online for the solutions but no luck.
Just a clue would suffice on how to answer the problem. Any help would be appreciated. Thank you.
finance economics
finance economics
asked Feb 1 at 15:16
JayceJayce
180111
asked Feb 1 at 15:16
JayceJayce
180111
asked Feb 1 at 15:16
JayceJayce
180111
asked Feb 1 at 15:16
JayceJayce
180111
asked Feb 1 at 15:16
JayceJayce
180111
180111
2
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49
add a comment |
2
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49
2
2
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$$100$ times the rate of return times $0.58$ (the amount after taxes) equals $$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07%$
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
$endgroup$
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3096342%2fminimum-rate-of-return%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$$100$ times the rate of return times $0.58$ (the amount after taxes) equals $$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07%$
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
$endgroup$
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
add a comment |
$begingroup$
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$$100$ times the rate of return times $0.58$ (the amount after taxes) equals $$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07%$
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
$endgroup$
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
add a comment |
$begingroup$
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$$100$ times the rate of return times $0.58$ (the amount after taxes) equals $$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07%$
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
$endgroup$
I always find it helps to convert the problem into words and use a convenient $100 starting sum such that the math becomes obvious. Instead of blindly guessing which standard formula to use, it helps in determining a correct formula and intuitively understanding the solution. With that.....
$$100$ times the rate of return times $0.58$ (the amount after taxes) equals $$7$
Here you can see why simply multiplying the two given percentages doesn't work. The quantity of interest is the amount remaining after taking out 42% in tax.
Now we can substitute the rate of return for $r$ and solve the equation.
$100r cdot 0.58 = 7$
$100r = 12.07$
$r = .1207$ or $12.07%$
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
answered Feb 1 at 16:38
Phil HPhil H
4,3102312
4,3102312
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
add a comment |
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
$begingroup$
Thank you for the very detailed explanation. I need to practice this kind of mentality when answering certain word problems.
$endgroup$
– Jayce
Feb 2 at 13:38
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3096342%2fminimum-rate-of-return%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
Don't blindly rely on formulas! If your pre-tax return is $r$ then your post-tax return is $.58times r$ (since you pay $.42times r$ in tax). Thus you want to solve $.58times r= 7$. Can you finish from here?
$endgroup$
– lulu
Feb 1 at 15:20
$begingroup$
Thanks for the fast response. While we get the correct answer from that equation. I don't really get why could just simply multiply or divide those percentages. At least I have encountered this kind of problem and I'll just remember how you answered it.
$endgroup$
– Jayce
Feb 1 at 15:49