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Bob invested one half of his savings in a bond that paid simple intere

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Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 21 Apr 2015, 04:45
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Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

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[Reveal] Spoiler: OA

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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 21 Apr 2015, 07:42
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Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.


First divide $550/2years to get 275$/yr non-compounding interest.

Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$275= $330.

To find the difference in interest gained, $330-$275= $55 increase in interest after the first year through compounding.

From this information we can set up the equation $275 * X% = $55... 55/275=1/5=20% giving us answer choice E.
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 21 Apr 2015, 08:37
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Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.


For the first year SimpleInterest and Compound interest will always be same if compounding is done annually.
So, the difference \(605 - 550 = 55\) is attributed to 275$ which accumulated at the end of 1st year in the CompoundInterest account.

\(275 * \frac{R}{100} = 55\)

\(R=20%\)
Answer E.
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 27 Apr 2015, 02:30
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.


CHECK VERITAS PREP OFFICIAL SOLUTION HERE:
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink]

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New post 06 Dec 2017, 13:14
Used hit and trial.
605 - 550 = 55 dollars

a) 5% of x is 25. So tried 10% (option B) --> it is $550

10% *550+500 = 605

Total interest = 10%+ 10%= 20 % interest

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Re: Bob invested one half of his savings in a bond that paid simple intere   [#permalink] 06 Dec 2017, 13:14
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