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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] New post 25 Oct 2006, 07:22
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Nov 2013, 03:24, edited 1 time in total.
Edited the question and added the OA.
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Answer D [#permalink] New post 25 Oct 2006, 07:35
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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 [#permalink] New post 09 Nov 2013, 12:23
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Re: Answer D [#permalink] New post 20 Nov 2013, 09:10
Damager wrote:
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


Any other way to solve this one? I tried something similar, but was curious if there are any other solutions.
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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 20 Nov 2013, 09:47
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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 that2r*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] New post 20 Nov 2013, 16:59
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 that2r*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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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 20 Nov 2013, 21:43
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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 that2r*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] New post 20 Nov 2013, 22:57
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] New post 20 Nov 2013, 23:05
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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] New post 21 Nov 2013, 05:26
mau5 wrote:
AccipiterQ wrote:

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


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



How did you get it to equal \frac{6}{5} though?

r*x*(1+r)=330
= rx+r^2x=330
...I don't see a 6/5 in there anywhere
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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 21 Nov 2013, 07:08
Expert's post
mau5 wrote:
AccipiterQ wrote:
mau5 wrote:
How did you get it to equal \frac{6}{5} though?

r*x*(1+r)=330
= rx+r^2x=330
...I don't see a 6/5 in there anywhere


Please read the reply above carefully

shawn-invested-one-half-of-his-savings-in-a-bond-that-paid-s-37333.html#p1295319
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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 21 Nov 2013, 07:14
mau5 wrote:



d'oh...330/275=6/5
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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 09 Jan 2014, 00:58
Please explain ---



r*x*(1+r)=330

How you take "r" in multiplication for 2nd year ..can you please clarify ??...

Else i understand your concept ...nice explanation
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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 09 Jan 2014, 05:30
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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Re: Shawn invested one half of his savings in a bond that paid s [#permalink] New post 09 Jan 2014, 06:19
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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] 09 Jan 2014, 06:19
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