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

Question

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

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

Damager · Accepted Answer

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

Bunuel · Answer

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.

mau5 · Answer

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} 	o r = \frac{1}{5}

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

A.

AccipiterQ · Answer

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...

mau5 · Answer

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.

I have assumed the initial amount to be 2x, not x.

smartyman · Answer

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

mau5 · Answer

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

TroyfontaineMacon · Answer

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

GyMrAT · Answer

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,
GyM

sriramsundaram91 · Answer

karlfurt : You should have added an option 1375$, people would have chosen that. It would have been more difficult.

fskilnik · Answer

?\,\,\,:\,\,\,{\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.

Karastoyanov · Answer

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

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