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Retired Moderator
Joined: 29 Apr 2015
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Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 30 Sep 2015, 11:15 4 1 13 00:00 Difficulty: 65% (hard) Question Stats: 66% (02:53) correct 34% (03:03) wrong based on 129 sessions ### HideShow timer Statistics John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 01 Oct 2015, 23:20 5 2 reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

$100 was invested in each fund. After one year, the difference in interest is$10. So this means, the rate of interest of fund A is 10% more than the rate of interest of fund B.
After 2 years, the difference in interest is $25. Out of this,$10 is the extra interest earned on principal in the first year, another $10 is the extra interest earned on principal in the second year and$5 is the extra interest earned on interest of the first year.

So if rate of interest in fund A is 20%, rate of interest in fund B is 10% and difference in interest earned on interest = 20% of 20 - 10% of 10 = 4 -1 = 3
If rate of interest in fund A is 30%, rate of interest in fund B is 20% and difference in interest earned on interest = 30% of 30 - 20% of 20 = 9 - 4 = 5 (Correct)

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##### General Discussion
Intern
Joined: 21 Jul 2015
Posts: 1
Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 30 Sep 2015, 23:08 2 reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60% ---------------------------------- we know Value of A after 1 year V1a = V1b+10 and after second year V2a = V2b+25 and initial amount is 100 for A and B Substitute from answers and check if it matches the above equations i always start with choice B.. B : 30 After 1 year Va1 = 130 = Vb1+10 => Vb1 = 120 => interest for B = 20 After 2nd year Va2 = 169 Vb2 = 144 it fits our equation Va2 = Vb2+25 so answer is B Substituting A:20 gives Va2-Vb2=23 but should be 25 C:40 => Va2-Vb2=27 Intern Joined: 29 Mar 2015 Posts: 22 John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

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01 Oct 2015, 18:36
4
The first part of the question tells us that there is a 10% difference between both rates:
If, let's say, the fixed rate of fund A was 40%, then the value would have increased to $140 in the first year. Fund B must have increased to$130 ($140 -$130 = $10) - thus fund B is appreciating at a fixed rate of 30%. Note how these rates translate into 1.4 (=1+40/100) and 1.3. I like to translate those into 14 and 13. The second piece of the question stems tell us that the difference between the squares of the two number is$25.
Squares because the formula for two years of annual compounding is (1+ r/100)^2.
What we are essentially looking for is a number X which square is 25 more than the square of the number X - 1.

$$x^2 - (x-1)^2 = 25$$
$$x^2 - x^2 + 2x - 1 = 25$$
$$x = 13$$

Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 01 Oct 2015, 23:37 4 1 reto wrote: John invested$100 in each of the funds A and B. After one year, the value of the money in fund A was $10 higher than the value of the money in fund B. After another year, the value of the money in fund A was$25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%

Hi,
since the increase is on 100$, the diff in values will be 10 so say A and B be the annual interest respectively... A-B=10.. or A=B+10.. now for second year.. $$\frac{100(100+A)(100+A)}{100^2}-\frac{100(100+B)(100+B)}{100^2}=25$$ (100+A)(100+A)-(100+B)(100+B)=2500... substitute A=B+10.... $$(110+B)^2-(100+B)^2=2500$$ or (110+B+100+B)(110+B-100-B)=2500 210+B=250 B=20.. so A=30 Ans B _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Intern Joined: 01 Aug 2015 Posts: 16 Location: India Concentration: Technology, Statistics GPA: 4 WE: Engineering (Computer Software) John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

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03 Oct 2015, 09:14
4
I think the quickest way to solve is through back solving,

we know
rA = rB +10
And after 2 years Amount(A) is higher than Amount(B) by 25$C) 40% so rB =30% Amount(A) = 100x(1.4)^2 Amount(B) = 100x(1.3)^2 ---------------- 27$ > 25$So rA must be less than 40%, so its A or B. A) 20% so rB =10% Amount(A) = 100x(1.2)^2 Amount(B) = 100x(1.1)^2 ---------------- 23$

B) 30%
so rB =10%
Amount(A) = 100x(1.3)^2
Amount(B) = 100x(1.2)^2
----------------
25$_________________ With the new day comes new strength and new thoughts. ~Eleanor Roosevelt _____________________________________________ Feel free to +1 Kudos if you like this post Retired Moderator Joined: 29 Apr 2015 Posts: 842 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) Re: John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

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04 Oct 2015, 00:17
3
reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60% Plugging in seems most efficient: Start with C: Fund A, Fund B 100, 100 140, 130 (A is 10 more, from the statement, hence 30% growth rate) 196, 169 (A is not$25 more as ist should be, --> let's go on with B, one lower because we need a lower difference).

Fund A, Fund B
100, 100
130, 120 (A is 10 more, as defined in the text, hence 20% p.a. growth rate).
169, 144 (Here we go, A is $25 higher, this is the solution). _________________ Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS! PS Please send me PM if I do not respond to your question within 24 hours. Intern Joined: 31 Aug 2014 Posts: 22 Re: John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

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07 Oct 2015, 11:43
4
reto wrote:
reto wrote:
John invested $100 in each of the funds A and B. After one year, the value of the money in fund A was$10 higher than the value of the money in fund B. After another year, the value of the money in fund A was $25 higher than the value of the money in fund B. If the value of the money in each fund increased by a fixed interest compounded annually, what was the annual interest of fund A? A. 20% B. 30% C. 40% D. 50% E. 60% Plugging in seems most efficient: Start with C: Fund A, Fund B 100, 100 140, 130 (A is 10 more, from the statement, hence 30% growth rate) 196, 169 (A is not$25 more as ist should be, --> let's go on with B, one lower because we need a lower difference).

Fund A, Fund B
100, 100
130, 120 (A is 10 more, as defined in the text, hence 20% p.a. growth rate).
169, 144 (Here we go, A is $25 higher, this is the solution). if rate of interest in fund A is 20%, rate of interest in fund B is 10% and difference in interest earned on interest = 20% of 20 - 10% of 10 = 4 -1 = 3 If rate of interest in fund A is 30%, rate of interest in fund B is 20% and difference in interest earned on interest = 30% of 30 - 20% of 20 = 9 - 4 = 5 (Correct) Answer (B) _________________ Please press+ 1kudos if you appreciate this post and for motivation !! Intern Joined: 27 Oct 2014 Posts: 2 Re: John invested$100 in each of the funds A and B. After one year, the v  [#permalink]

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08 Oct 2015, 20:45
1
Greetings Everyone!

Had no interest in solving by the use of formulae which have already been stated brilliantly in the above posts.
So I used the tragic method of trial and error.

As stated in the question, the interest is compounded. It's also easy to spot the words "fixed interest rates and $10,$25" differences. A quick glance at the options and you might get a gist of the answer that awaits.

A $10 difference will point to the rates being 10% apart. But what's also given is that the rates will differ by$25 the next year. So compounding the rates, you'll notice that at 30 you get $169 in the second, whilst a 10% gap to 20% at which fund B will be computed, and you will realize that the amount comes to$144.
After 1st year (130 * 30%) and ($120* 20%). 130 and 120 are amounts with interests from the first year. So an exact$25 difference arises and problem == solved.

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Joined: 09 Sep 2013
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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink] ### Show Tags 30 May 2018, 07:57 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: John invested$100 in each of the funds A and B. After one year, the v &nbs [#permalink] 30 May 2018, 07:57
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