GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2018, 05:55

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49965
Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

21 Apr 2015, 05:45
2
10
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:29) correct 41% (03:00) wrong based on 169 sessions

### HideShow timer Statistics

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.

_________________
Director
Joined: 07 Aug 2011
Posts: 549
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

21 Apr 2015, 09:37
5
2
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.

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. _________________ Please pass me a +KUDOS if you liked my post! Thanks! Do not compare yourself to others, compare yourself to who you were yesterday. Math Expert Joined: 02 Sep 2009 Posts: 49965 Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] ### Show Tags 27 Apr 2015, 03:30 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: _________________ Senior Manager Joined: 15 Jan 2017 Posts: 363 Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] ### Show Tags 06 Dec 2017, 14:14 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
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 267
Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

28 Mar 2018, 08:38
in the first year interest earned from both bonds will remain the same, thus
interest earned from both bonds in the first year is

550 / 2 = 275

so, in the second year, interest earned from the bond that pays compounded interest will be (605 - 275) = 330

now, the extra amount (330 - 275) = 55 is the interest earned on the interest of previous year's interest

so, 55 = i * 275

=) i = 55 / 275

thus interest rate is 1/5 = 20 % = E the answer

thanks
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

09 Apr 2018, 16:30
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%

Although we are not given the amount invested in either of the two bonds,, we know that the two amounts are equal. So we can let P = the amount invested in each bond. We can let r = the interest rate for each bond investment. We can create an equation for the amount of interest earned for the first bond, using the simple interest formula P x r x t = I. :

P x r x 2 = 550

We can also create an equation for the amount of interest earned for the second bond, using the compound interest formula: P(1 + r)^t - P = I:

P(1 + r)^2 - P = 605

Simplifying the first equation, we have P(2r) = 550 and simplifying the second equation, we have P[(1 + r)^2 - 1] = 605. Dividing the first equation by the second, we see that the P cancels out, and we have:
(2r)/[(1 + r)^2 - 1] = 550/605

605(2r) = 550[(1 + r)^2 - 1]

1210r = 550[1 + 2r + r^2 - 1]

1210r = 1100r + 550r^2

110r = 550r^2

Dividing both sides by 110r, (we can do that since r is nonzero), we have:

1 = 5r

r = 1/5 = 20%

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

07 May 2018, 19:07
JeffTargetTestPrep wrote:
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%

Although we are not given the amount invested in either of the two bonds,, we know that the two amounts are equal. So we can let P = the amount invested in each bond. We can let r = the interest rate for each bond investment. We can create an equation for the amount of interest earned for the first bond, using the simple interest formula P x r x t = I. :

P x r x 2 = 550

We can also create an equation for the amount of interest earned for the second bond, using the compound interest formula: P(1 + r)^t - P = I:

P(1 + r)^2 - P = 605

Simplifying the first equation, we have P(2r) = 550 and simplifying the second equation, we have P[(1 + r)^2 - 1] = 605. Dividing the first equation by the second, we see that the P cancels out, and we have:
(2r)/[(1 + r)^2 - 1] = 550/605

605(2r) = 550[(1 + r)^2 - 1]

1210r = 550[1 + 2r + r^2 - 1]

1210r = 1100r + 550r^2

110r = 550r^2

Dividing both sides by 110r, (we can do that since r is nonzero), we have:

1 = 5r

r = 1/5 = 20%

QUESTION:

Why did you divide the first equation by the second?
Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

07 May 2018, 19:16
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.

When it asks for the "annual rate of interest" I am under the assumption that there are two different bonds--(1) one that pays simple interest and (2) one that pays compound interest. How can there only be one annual rate of interest? Thank you.
Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

### Show Tags

07 May 2018, 19:23
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.

Believe I may have answered my own question. One of the insights is to realize that though given two equations and two unknowns (P and r), the Ps cancel out leaving two equations and one unknown, therefore, one can solve for r, that annual rate of interest? Thanks.
Re: Bob invested one half of his savings in a bond that paid simple intere &nbs [#permalink] 07 May 2018, 19:23
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.