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Shawn invested one half of his savings in a bond that paid s

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Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post Updated on: 10 Nov 2013, 04:24
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Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000

Originally posted by karlfurt on 25 Oct 2006, 08:22.
Last edited by Bunuel on 10 Nov 2013, 04:24, edited 1 time in total.
Edited the question and added the OA.
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Answer D  [#permalink]

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New post 25 Oct 2006, 08:35
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CI means SI for 1st year + SI for 2nd Year + SI on (SI for 2nd year)

SI for 1st year = 550/2=275

275+275+SI on (275)=605==> SI on 275=55==>
SI on 275 = 275*R*1/100=55
R=20%

Now using SI for 2 years on T/2 of the money

(T/2)*20*2/100=550
T=550*5= 2750
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 20 Nov 2013, 10:47
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karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then \(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

Thus,\((1+r) = \frac{6}{5} \to r = \frac{1}{5}\)

Replacing this in the second equation, we get \(2x = \frac{550}{r} = 550*5 = 2750\)

A.
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 20 Nov 2013, 17:59
mau5 wrote:
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then \(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

Thus,\((1+r) = \frac{6}{5} \to r = \frac{1}{5}\)

Replacing this in the second equation, we get \(2x = \frac{550}{r} = 550*5 = 2750\)

A.


wait how did you know that \((1+r) = \frac{6}{5}\)


also where do you get \(2x = \frac{550}{r} = 550*5 = 2750\) from? Is there a lot of work you did in your head?

Because if you sub in 1/5 for R, then you end up with 2x=550/(1/5) and then 2x=2750, and x=1375, not 2750...
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New post 20 Nov 2013, 22:43
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AccipiterQ wrote:

wait how did you know that \((1+r) = \frac{6}{5}\)


\(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

Replace the value of r*x from the second equation in the first.

AccipiterQ wrote:
also where do you get \(2x = \frac{550}{r} = 550*5 = 2750\) from? Is there a lot of work you did in your head?

Because if you sub in 1/5 for R, then you end up with 2x=550/(1/5) and then 2x=2750, and x=1375, not 2750...


I have assumed the initial amount to be 2x, not x.
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 20 Nov 2013, 23:57
Please explain:
Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks.
Simple interest formula: I = PRt
550 = PR2
550/2P = R

Compound interest formula: P + I = P(1+R)^t
P + 605 = P(1+R)^2
P + 605 = P(1 + 2(550/2P) + (550/2P)^2)
P + 605 = P + 550/2 + (550)^2/ 4P
55 = (550)^2/4P
P = 2750
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 21 Nov 2013, 00:05
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smartyman wrote:
Please explain:
Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks.


Say you have 200 $. Half of it is getting you simple interest per year at 10% rate.Thus, the interest you earn for the first year : \(\frac{10}{100}*100 = 10 $\)

Now, the other half is getting you compound interest at 10%, where interest is again compounded annually.Thus, the interest from the first year : \(\frac{10}{100}*100 = 10 $\)

Now, suppose I told you that the total CI you got from the other half for 2 years was 40 $, then the interest you earned from the second year is nothing but : 40-10 = 30$

The same has been done above. Note that as the rate of interest and the time is the same for both CI and SI, the interest earned for the first year will be exactly same in either case.

Hope this helps
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 09 Jan 2014, 06:30
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karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Tough problem omg!

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

but

after that....I AM LOST!!!!

HELP HELP HELP
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New post 09 Jan 2014, 07:19
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TroyfontaineMacon wrote:
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Tough problem omg!

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

but

after that....I AM LOST!!!!

HELP HELP HELP


So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $275, thud 0.2x = $275 --> x = $1,375.

Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,375 = $2,700.

Answer: A.
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 24 Jun 2018, 01:02
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let Shawn's Total Savings = 2X

He invests X amount at simple interest for 2 years at "r" rate of interest & receives $550 as interest.

550 = X * 2 * r

Xr = 275..........................(i)

He invests X amount at compound interest for 2 years at same "r" rate of interest & receives $605 as interest.

In year one,

Interest on amount X = Xr

In year two,

Interest on amount X + Xr = (X + Xr) * r = Xr + Xr^2

Total interest for 2 years = Xr + Xr + Xr^2 = 2Xr + Xr^2


Hence we have, 2Xr + Xr^2 = 605

2*275 + 275*r = 605

Solving we get, r = 1/5

Hence X = 275 * 5 = 1375

Therefore the Total Savings = 2X = 2*1375 = 2750

Answer A.


Thanks,
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 05 Aug 2018, 11:20
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karlfurt: You should have added an option 1375$, people would have chosen that. It would have been more difficult.
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Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 30 Jan 2019, 12:33
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000

\(?\,\,\,:\,\,\,{\rm{money}}\,\,{\rm{invested}}\,\,{\rm{in}}\,\,{\rm{both}}\,\,{\rm{bonds}}\)

For the simple interest savings, Shawn received $275 for the first year and that´s exactly the same amount paid at the end of the first year in the bond with annually compounded interest.

Subtracting $550 (simple interest) from $605 (compounded interest), both received after 2 years, $55 is the compounded interest in one-year period, hence the annual interest rate is equal to 55/275 = 1/5 = 20%.

The $550 simple interest obtained by the 20% annual interest rate represents 2/5 of the amount invested in the bond that paid simple interest, hence 5/2 * 550 = $1,375 is the amount invested in that bond.

Finally, our focus is twice the last value (hence $2750).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

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New post 14 May 2019, 13:48
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I think that it's not real to solve it in 2 min... although GMAT assassins aren't born, they're made :)

Here is my solution (detailed):

1. 550/2=275. 275 is the amount that Shawn got as a 1st year interest. In first year simple or compound interests are the same;
2. 605-275=330 - we need to find this number to understand interest on interest i.e. by which % these 275 from the first year grew => so they grew from 275 to 330;
3. (330-275)/275=0,2 i.e. 20% - we find an interest rate (in step 2 we found the amount and in this step, we found the interest itself);
4. 275/0,2=1375 the amount that was initially invested (if 275 is 20%, the whole amount is 275/0,2);
5. 1375*2=2750 - we multiply by 2 because there were 2 amounts.
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Re: Shawn invested one half of his savings in a bond that paid s   [#permalink] 14 May 2019, 13:48
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