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John invested $100 in each of the funds A and B. After one year, the v

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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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New post 30 Sep 2015, 12:15
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A
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E

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Question Stats:

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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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New post 01 Oct 2015, 00:08
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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 Va2-Vb2=23 but should be 25
C:40 => Va2-Vb2=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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New post 01 Oct 2015, 19:36
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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.

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

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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New post 02 Oct 2015, 00:20
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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%


$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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New post 02 Oct 2015, 00:37
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
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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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New post 03 Oct 2015, 10:14
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$
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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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New post 04 Oct 2015, 01:17
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).
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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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New post 07 Oct 2015, 12:43
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)
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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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New post 08 Oct 2015, 21:45
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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Re: John invested $100 in each of the funds A and B. After one year, the v [#permalink]

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Re: John invested $100 in each of the funds A and B. After one year, the v   [#permalink] 30 May 2018, 08:57
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