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On what sum will the difference between the simple and compound interest for 3 years at 5 percent per annum amount to Rs. 24.40?
On what sum will the difference between the simple and compound interest for 3 years at 5 percent per annum amount to Rs. 24.40?
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[Solved] On what sum will the difference between the simple interest
Rate = 5% Time = 3 years Let the principal be = P Difference between C.I and S.I = Rs. 12.20 \(\begin{array}{l} \Rightarrow {\rm{C}}.{\rm{I}} - {\rm{S}}.{\r
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On what sum of money will the difference between the compound interest & simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5 % p.a.?
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Solution
The correct option is B
Rs.10000
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Intern
Joined: 27 Dec 2013
Posts: 30
Concentration: Finance, General Management
On what sum will the difference between simple and compound [#permalink]
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Hi,
I am unable to solve the below mentioned question as well not able to understand thr answer that is provided. request members and experts to provide solution.
On what sum will the difference between simple and compound interest for 3 years at 5 percent per annum amount to 12.20?
answer is
1600.
thanks and regards,
harish
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4464
Re: problem on simple interest and compund interest combined [#permalink]
harishbiyani wrote:
Hi,
I am unable to solve the below mentioned question as well not able to understand thr answer that is
provided. request members and experts to provide solution.
On what sum will the difference between simple and compound interest for 3 years at 5 percent per annum amount to 12.20?
answer is 1600.
thanks and regards,
harish
Dear Harish,
I'm happy to help.
First of all, I'll say watch the free Magoosh blog,
//magoosh.com/gmat/
because I just wrote an extensive article on simple & compound interest, with practice questions, and that will go live on the blog in a week or so.
Understand, first of all, that this question is not really a GMAT question as is, because it would require a calculator to solve. If five answer choices were given, we would be able to use backsolving to determine an answer. See:
//magoosh.com/gmat/2013/backsolving-on-gmat-math/
I will just start with the value $1600 and backsolve from this, showing that it works. First, simple interest.
1% of 1600 is $16, so 5% is 5*16 = $80. That's simple interest for one year. In three years, that's 3*80 = $240.
Now, compound interest. The amount will experience a 5% increase three times. The multiplier for a 5% increase is 1.05. For more on percent increases as multipliers, see:
//magoosh.com/gmat/2012/understand ... -the-gmat/
The total amount, principle plus compound interest, after three years is
1600*(1.05)^3 = $1852.20
(I used a calculator for that.)
That's $252.20 in interest. That's a 252.20 - 240 = $12.20 difference between simple & compound interest.
Understand, my friend, it's very very easy to create compound interest questions that only could be solved with a calculator. It's a bit trickier to write high quality compound interest questions that can be solved entirely without a calculator, which are amenable to estimation and backsolving and other approximation methods. The blog that will be release on the Magoosh blog in a week or so will have a few high quality questions of this sort. Here's another question of that order:
Cindy invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?
(A) $10079.44
(B) $10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Let me know if you would like an explanation of this question.
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
GMAT Expert
Joined: 16 Oct 2010
Posts: 13197
Location: Pune, India
Re: problem on simple interest and compund interest combined
[#permalink]
harishbiyani wrote:
Hi,
I am unable to solve the below mentioned question as well not able to understand thr answer that is
provided. request members and experts to provide solution.
On what sum will the difference between simple and compound interest for 3 years at 5 percent per annum amount to 12.20?
answer is 1600.
thanks and regards,
harish
To solve this question, you need to understand how simple and compound interest are different. Note that it is easy to solve for their difference after 2 years but it gets trickier as you increase the number of years. I have discussed
these concepts in this post: //www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html?/2011/03 ... imple-one/
Compound interest differs by simple in that it gives interest on interest earned too. In the first year, both compound and simple give the same
interest (assuming annual compounding). In the second year, compound interest includes interest on the interest earned in the first year too.
Say, initial amount is D.
______________SI____________________CI
1st year______0.05D_________________0.05D
2nd Year____2*0.05D________________2*0.05D + 0.05*0.05D (Interest earned on last year's interest)
3rd Year____3*0.05D________________3*0.05D + 0.05*0.05D + .05(2*0.05D + 0.05*0.05D) [Interest on
principal this year +Last year's interest + interest on last year's interest]
The difference in the SI and CI in third year is
0.05*0.05D + .05(2*0.05D + 0.05*0.05D) = 12.2
(25/10000)(3D + 0.05D) = 12.2
D = 4880/3.05
If you assume the denominator is 3, you get 1600 something. Ignore the something since denominator is greater than 3 to get 1600.
_________________
Karishma
Owner of Angles and Arguments
Check out my Blog Posts here:
Blog
For Individual GMAT Study Modules, check Study Modules
For Private Tutoring, check Private Tutoring
Intern
Joined: 27 Dec 2013
Posts: 30
Concentration: Finance, General Management
Re: problem on simple interest and compund interest combined
[#permalink]
mikemcgarry wrote:
Understand, my friend, it's very very easy to create compound interest questions that only could be solved
with a calculator. It's a bit trickier to write high quality compound interest questions that can be solved entirely without a calculator, which are amenable to estimation and backsolving and other approximation methods. The blog that will be release on the Magoosh blog in a week or so will have a few high quality questions of this sort. Here's another question of that order:
Cindy invests
$10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?
(A) $10079.44
(B) $10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Let me know if you would like an explanation of this question.
Mike
Hi Mike,
Thanks for your
explanation. It was helpful.
Regarding this question that you have posted; is the answer Option B?
This is how i calculated the answer:
= 10,000*101.98/100*101.98/100*101.98/100*101.98/100
= 10.198 * 10.198 * 10.198 * 10.198
~ 10.2 * 10.2 * 10.2 * 10.2
~ 10816
The approximated answer is 10, 816 so i choose option B
Let me know if there is any other faster way to answer this question. It would be great to learn.
Also, could you please tell me
what was the level of the question?
Thanks,
Harish
Intern
Joined: 27 Dec 2013
Posts: 30
Concentration: Finance, General Management
Re: problem on simple interest and compund interest combined [#permalink]
Thanks Krishna for your explanation too.
I had never used this method before. I hope, i can use your method in some complex
problems.
Thanks and Regards,
Harish
GMAT Expert
Joined: 16 Oct 2010
Posts: 13197
Location: Pune, India
Re:
problem on simple interest and compund interest combined [#permalink]
harishbiyani wrote:
Thanks Krishna for your explanation too.
I had never used this method before. I hope, i can use your
method in some complex problems.
Thanks and Regards,
Harish
Ok, then use the method I discussed above to solve the question given by Mike orally. Think - what is the difference between SI and CI? What happens to this difference if rate of interest is very low such as approx 2%? Can you easily approximate the answer without lifting a finger?
_________________
Karishma
Owner of Angles and Arguments
Check out my Blog Posts here:
Blog
For Individual GMAT Study Modules, check Study Modules
For Private Tutoring, check Private Tutoring
Intern
Joined: 27 Dec 2013
Posts: 30
Concentration: Finance, General Management
Re: problem on simple interest and compund interest combined
[#permalink]
I mis- spelled your name as Krishna instead of Karishma.
Sorry for that.
Re: problem on simple interest and compund interest combined [#permalink]
16 Jan 2014, 22:55
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