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

 It is currently 06 Dec 2019, 20:29 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # An investment of d dollars at k percent simple annual

Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 08 Nov 2010
Posts: 268
An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

10
62 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:21) correct 25% (02:28) wrong based on 837 sessions

### HideShow timer Statistics

An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,400 over a 3 year period?

A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

24
28
An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,4,00 over a 3 year period?
A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3

Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate.

An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period --> $$d*\frac{k}{100}*2=600$$ --> $$k=\frac{30,000}{d}$$ What (x) dollar amount invested at the same rate will yield$2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$.

Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3.

_________________
Intern  Joined: 05 Jan 2012
Posts: 43
Schools: Wharton '15
WE: Sales (Internet and New Media)
Re: An investment of d dollars at k percent  [#permalink]

### Show Tags

6
5
Since you want to earn 4 times more interest in 1.5 times the current time period, the answer will be 4d/1.5 or 8d/3
##### General Discussion
Senior Manager  Joined: 08 Nov 2010
Posts: 268
Re: Another simple one i guess...  [#permalink]

### Show Tags

Thanks. Didnt know the Simple interest thing.

+1 from me for all ur help.

thanks.
Current Student Joined: 26 May 2005
Posts: 443
Re: an investment of d dollars at k percent  [#permalink]

### Show Tags

1
WishMasterUA wrote:
an investment of d dollars at k percent simple annual interest yield $600 interest over a 2-year period. in term of d, what dollar amount invested at the same rate will yild$2400 interest income over a 3-year period?
1) 2d/3
2) 3d/4
3) 4d/3
4) 3d/2
5) 8d/3

Please explain in detail how to solve this problem.

simple interest = PNR/100
dk2=600
d = 300/k
thus
(x*300/k)*k*3= 2400
X= 2400/900= 24/9 = 8/3

hence E
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

1
1
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54

_________________
Intern  Joined: 03 Feb 2011
Posts: 13
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

Hi Bunuel,

If we take simple annual interest of 2% for $10,000 investment, for 2 years it will amount to$404.

How do we know "An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period" = d*k/100 *2 and not similar to$404 calc?

Thanks
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

3
6
Hi nitestr,

The GMAT will likely ask you to deal with an "interest formula" question once or twice, so you need to note the wording of the prompt and you need to know the formulas for simple interest and compound interest.

Simple Interest = (Principal)(1 + RT)

Compound Interest = (Principal)(1 + R)^T

R = interest rate written as a decimal
T = length of time (usually years)

So, if we calculate 2% simple interest on a $10,000 principal over 2 years, we'll have... (10,000)(1 + (.02)(2)) (10,000)(1.04) = 10,400 The interest = 400 (not 404) GMAT assassins aren't born, they're made, Rich _________________ Intern  Joined: 03 Dec 2014 Posts: 14 GMAT 1: 620 Q43 V32 GPA: 2.9 Re: An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 1 EMPOWERgmatRichC wrote: Hi nitestr, The GMAT will likely ask you to deal with an "interest formula" question once or twice, so you need to note the wording of the prompt and you need to know the formulas for simple interest and compound interest. Simple Interest = (Principal)(1 + RT) Compound Interest = (Principal)(1 + R)^T R = interest rate written as a decimal T = length of time (usually years) So, if we calculate 2% simple interest on a$10,000 principal over 2 years, we'll have...

(10,000)(1 + (.02)(2))
(10,000)(1.04) = 10,400
The interest = 400 (not 404)

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

The formula for the Simple interest is S.I = Principal (RT) no ?

Regards
S
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

3
Hi SD007,

If you want to calculate the amount of simple interest generated, then YES, the calculation is...

(Principal)(RT)

If you're interested in the TOTAL amount of money (e.g. in a bank account) AFTER the simple interest is generated, then the calculation is....

(Principal)(1 + RT)

GMAT assassins aren't born, they're made,
Rich
_________________
Intern  Joined: 14 Mar 2015
Posts: 16
Location: India
Concentration: General Management, Strategy
Schools: ISB '18, IIMA , IIMB
GPA: 3.53
WE: Engineering (Other)
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

7
Simple way to solve it -
600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money. Answer is E.
Senior Manager  B
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A$) GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 1 1 144144 wrote: An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? A. (2d)/3 B. (3d)/4 C. (4d)/3 D. (3d)/2 E. (8d)/3 Hi guys, I just did my first CAT and this one was the first question that I answered correctly. We don't need to involve any intetrest formulas at all here: the ratio of interest earnings per year = $$\frac{800}{300} = \frac{8}{3}$$ so the ratio of the investment that generates 2400 (let it be X) to D is the same (interest rate remains the same) $$\frac{8}{3}$$=$$\frac{x}{d}$$ --> $$x=\frac{8}{3}*d$$ Answer E GMAT Club Legend  V Joined: 12 Sep 2015 Posts: 4125 Location: Canada Re: An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 2 1 Top Contributor 1 144144 wrote: An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? A. (2d)/3 B. (3d)/4 C. (4d)/3 D. (3d)/2 E. (8d)/3 An investment of d dollars at k percent simple annual interest yields$600 over a 2-year period.
In other words, an investment of d dollars yields $300 in interest each year. What dollar amount invested at the same rate will yield$2,400 interest over a 3-year period?
In other words, how much money must we invest to earn $800 in interest EACH YEAR? If a d dollar investment yields$300 in interest EACH YEAR, then:
- a 2d dollar investment would yield $600 (2 times$300) in interest EACH YEAR
- a 3d dollar investment would yield $900 (3 times$300) in interest EACH YEAR
- a 4d dollar investment would yield $1200 (4 times$300) in interest EACH YEAR
- etc.

From here there are two approaches.

APPROACH #1
We want the ANNUAL interest to be $800. This means we must invest an amount that is BETWEEN 2d dollars and 3d dollars [since$800 is BETWEEN $600 and$900].
When we check the answer choices, only E, which can be written as (8/3)d, is BETWEEN 2d dollars and 3d
So, the correct answer must be E

APPROACH #2
To increase the ANNUAL interest from $300 to$800, we must invest 800/300 TIMES as much money.
800/300 = 8/3, so we must invest (8/3)d dollars [aka 8d/3 dollars]

Cheers,
Brent
_________________
Intern  B
Joined: 02 Feb 2014
Posts: 36
Concentration: Finance, General Management
GPA: 3.5
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

Bunuel wrote:
An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,4,00 over a 3 year period?
A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3

Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate.

An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period --> $$d*\frac{k}{100}*2=600$$ --> $$k=\frac{30,000}{d}$$ What (x) dollar amount invested at the same rate will yield$2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$.

Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3.

Bunuel.

I'm more interested in the "Another way" to solve it. I get the "4 times more" but I can't get to the "1.5 times longer". How do you calculate this?

Thanks.

Best.
_________________
"The stock market is filled with individuals who know the price of everything, but the value of nothing." - Philip Fisher
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

MarkHanna wrote:
Bunuel wrote:
An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,4,00 over a 3 year period?
A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3

Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate.

An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period --> $$d*\frac{k}{100}*2=600$$ --> $$k=\frac{30,000}{d}$$ What (x) dollar amount invested at the same rate will yield$2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$.

Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3.

Bunuel.

I'm more interested in the "Another way" to solve it. I get the "4 times more" but I can't get to the "1.5 times longer". How do you calculate this?

Thanks.

Best.

(3 year period)/(2 year period) = 1.5.
_________________
Intern  B
Joined: 02 Feb 2014
Posts: 36
Concentration: Finance, General Management
GPA: 3.5
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

Thank you Bunuel! _________________
"The stock market is filled with individuals who know the price of everything, but the value of nothing." - Philip Fisher
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: An investment of d dollars at k percent simple annual  [#permalink]

### Show Tags

1
144144 wrote:
An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,400 over a 3 year period?

A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3

Recall that the amount of simple interest, I, is equal to the principal, P, times the annual interest rate, r, times the number of years, t. That is, I = Prt.

We are given that I = 600, P = d, r = k/100 and t = 2, so we have:

600 = d(k/100)(2)

300 = dk/100

dk = 30,000

What (x) dollar amount invested at the same rate will yield $2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$. Answer: E. Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3. Answer: E. hi pushpitkc - one question, why do we multiply by 2 like this $$d*\frac{k}{100}*2=600$$ shoudnt we put 2 as exponent as per formula $$600 = d(1+\frac{k}{100})^2$$ can you explain why am i thining so ? thankns! D Senior PS Moderator V Joined: 26 Feb 2016 Posts: 3300 Location: India GPA: 3.12 An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 1 dave13 wrote: Bunuel wrote: An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,4,00 over a 3 year period? A. (2d)/3 B. (3d)/4 C. (4d)/3 D. (3d)/2 E. (8d)/3 Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate. An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period --> $$d*\frac{k}{100}*2=600$$ --> $$k=\frac{30,000}{d}$$

What (x) dollar amount invested at the same rate will yield \$2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$.

Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3.

hi pushpitkc -

one question, why do we multiply by 2 like this $$d*\frac{k}{100}*2=600$$ shoudnt we put 2 as exponent as per formula $$600 = d(1+\frac{k}{100})^2$$

can you explain why am i thining so ? thankns!
D

Hey dave13

This problem deals with simple interest.
The formula for simple interest - Principal * Interest * $$\frac{R}{100}$$ where R is Rate of interest

Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got An investment of d dollars at k percent simple annual   [#permalink] 30 May 2018, 12:45

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by

# An investment of d dollars at k percent simple annual  