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Julie put half of her savings in a savings account that pays

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Julie put half of her savings in a savings account that pays  [#permalink]

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New post 12 Jul 2014, 07:11
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Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 12 Jul 2014, 11:43
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goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440


$120 for 2 years = $60 per year.

Extra $6 yearned with the compound interest is the percent yearned on percent. So, $6 is yearned on $60, which means that the interest = 10%.

This on the other hand means that half of the savings = 60*10 = $600. Twice of that = $1,200.

Answer: D.
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 12 Jul 2014, 08:03
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goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440


We need to find the amount off Julie's Initial savings...Let that be 2x

So x goes in simple interest and x goes in compund interest for a period of 2 years...

In case of Simple interest, The interest paid out is same for each year..Hence if $120 was interest for 2 years that means interest per year will be 60 $

So we have S.I,120 = \(\frac{x*2*R}{100}\)

or 6000 =x*R

For CI, in 126 $, 6$ represents nothing but interest earned on interest of 1st year.

In the First year, Interest amount is same for S.I and C.I

So we have

\(x(1+\frac{R}{100})^2-x= 126\)

or x(1 + R^2/10000+ 2R/100)-x=126

x+xR^2/10000+2xR/100)-x=126

x+R*6000/10000+12000/100-x=126

0.6R+120=126

0.6R=6 or R=10

So x=600...2x=1200 is the Initial savings.
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 12 Jul 2014, 09:25
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goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440


this question can also be solved by using less of math and more of logic.

simple interest earn for both of the years will remain same, whereas the compound interest earn will be different. Apart from that compund interest as well as the simple interest earn in the first year will be same.
for second year, simple interest will be p*r/100

computed interest will be p*r/100+p*r^2/(100)^2

and difference between these two equations = 6 (126-120)

thus we have, p*r^2=6*10000,
thus p=600 and r=10
since total amount=2p, thus correct answer will be 1200
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 14 Mar 2016, 22:40
goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440

$120 is simple interest for 2 years. $60 is 1 year SI. 126-120=$6 is the interest on the first year interest of $60.
That implies the rate of interest is 10%
for 10% the interest is 6 and principal is 60
for 100% the principal is 600
Therefore, the total investment is 2*600=$1200
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 13 Apr 2016, 18:15
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goodyear2013 wrote:
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

A) 600
B) 720
C) 1080
D) 1200
E) 1440


we can see: 120$ for 2 years, so 60$/year simple compound.
we then see 126$ annual compound, so 1st year will be 60$, second 66$. most likely looks like 10% interest.
say 600$ simple interest...10%=60, twice = 120. so works
600$ = compounded annually 1st year 660, second 726 so works.

initially, she had 600+600=1200$.
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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New post 25 Jun 2017, 09:52
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Simple interest earned for 2 years = $120, so the interest for the first year = $60.
Since compound interest starts compounding only from the second year, the compound interest for the first year will be the same as the simple interest = $60.

Option D fits the bill.
Initial savings = $1200, $600 in SI and $600 in CI.
SI at 10% p.a. for 2 years = $120.
CI at 10% p.a. for 2 years = $126.

Ans - D.
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Re: Julie put half of her savings in a savings account that pays  [#permalink]

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