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John invested $100 in each of the funds A and B. After one year, the v [#permalink]
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30 Sep 2015, 11:15
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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]
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30 Sep 2015, 23:08
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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 Va2Vb2=23 but should be 25 C:40 => Va2Vb2=27



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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
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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.
\(x^2  (x1)^2 = 25\) \(x^2  x^2 + 2x  1 = 25\) \(x = 13\)
Thus, the answer is 30%.



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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink]
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01 Oct 2015, 23:20
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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) Answer (B)
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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink]
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01 Oct 2015, 23:37
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... AB=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+B100B)=2500 210+B=250 B=20.. so A=30 Ans B
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John invested $100 in each of the funds A and B. After one year, the v [#permalink]
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03 Oct 2015, 09:14
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I think the quickest way to solve is through back solving, we know rA = rB +10 And after 2 years Amount(A) is higher than Amount(B) by 25$ 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$
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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
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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 B100, 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 B100, 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).
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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
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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 B100, 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 B100, 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)
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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
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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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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink]
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