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Alan has split his savings equally into two accounts. The

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Alan has split his savings equally into two accounts. The  [#permalink]

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New post 15 Jul 2014, 08:33
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Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 15 Jul 2014, 09:03
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goodyear2013 wrote:
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined


Let the amounts deposited on both accounts be $100.

Then we'd have that \(100 + 100*0.22 + 100*0.22=100(1+r)^2\) --> \(144=100(1+r)^2\) --> \((1+r)^2=1.44\) --> \(1+r=1.2\) --> \(r=0.2\).

Answer: D.
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 06 Apr 2016, 13:26
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plug in the values by considering a random value like 100 as the principal we get that only option D gives us the value of 44 as interest which we can calculate for the amount in question
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 23 Jun 2017, 17:35
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goodyear2013 wrote:
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined


We can actually solve this question because know that both principal amounts ( the two savings amounts that have been split and accumulated interested) are equal. So

Simple Interest = pv(1 +(t)(r)) = 100(1 + (.22)(2) = 144

Compounded interest= pv(1 +r)^t 100(1 + x/100)^2 = 144

x= 20

Thus
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 11 Jul 2017, 09:23
Suppose Alan split $200 into the two accounts. The first one with simple interest would be 100*(0.22+0.22)=144. To make the second one equal to the first one, we have 100*(1+r%)^2=144 ---> (1+r%)^2 = 1.44 = (1+20%)^2 ---> r=20
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 02 May 2018, 16:00
The algebra on this makes sense in the case of it only being compounded once annually...but we weren't given how many times per year it compounds. How can we assume just once, especially when one of the answer choices are "cannot be determined"?
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 02 May 2018, 23:02
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jsheppa wrote:
The algebra on this makes sense in the case of it only being compounded once annually...but we weren't given how many times per year it compounds. How can we assume just once, especially when one of the answer choices are "cannot be determined"?



Hi jsheppa

The specific details will be mentioned in the problem if the interest is compounded semi-annually
or quarterly. If we are not given any detail in the question, you can assume it to be annual!

An example of such a question
https://gmatclub.com/forum/leona-bought ... 43742.html

Hope this helps you
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Alan has split his savings equally into two accounts. The  [#permalink]

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New post Updated on: 17 Aug 2019, 03:46
Bunuel wrote:
goodyear2013 wrote:
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined


Let the amounts deposited on both accounts be $100.

Then we'd have that \(100 + 100*0.22 + 100*0.22=100(1+r)^2\) --> \(144=100(1+r)^2\) --> \((1+r)^2=1.44\) --> \(1+r=1.2\) --> \(r=0.2\).

Answer: D.

Originally posted by alekhyamaddila93@gmail.com on 17 Aug 2019, 02:17.
Last edited by alekhyamaddila93@gmail.com on 17 Aug 2019, 03:46, edited 1 time in total.
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 17 Aug 2019, 02:56
goodyear2013 wrote:
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined


Given: Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest.

Asked: If both accounts have the same balance after two years, what is the value of r?

Principal amount is same for both accounts = P
For simple interest account interest after 2 years = .22*2P = .44P
Balance after 2 years = P + .44P = 1.44P

For compound interest account
Balance after 2 years = P (1+r)^2

Since both accounts have the same balance after 2 years

P (1+r)^2 = 1.44 P
(1+r)^2 = 1.44
r =.2 = 20%

IMO D
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Re: Alan has split his savings equally into two accounts. The  [#permalink]

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New post 09 Jan 2020, 21:19
I figured it out this way:

22% simple interest; x% compound interest; both apply to equal principals and end up being the same amount by year's end. If compound interest = simple interest, the amount after one year under compound will be slightly higher, so the unknown compound interest here must be slightly lower than 22% to produce equal amounts.

Ans: 20%
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Re: Alan has split his savings equally into two accounts. The   [#permalink] 09 Jan 2020, 21:19
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