Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 Nov 2016
Posts: 1

A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
Updated on: 25 Jan 2017, 06:03
Question Stats:
62% (02:10) correct 38% (02:03) wrong based on 128 sessions
HideShow timer Statistics
A merchant invested $10,000 at 5% annual interest, compounded semiannually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X? a. $10,000 b. $10,125 c. $10,250 d. $10,500 e. $10,825
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by magniv123 on 25 Jan 2017, 02:48.
Last edited by Bunuel on 25 Jan 2017, 06:03, edited 1 time in total.
Renamed the topic, edited the question, moved to PS forum and added the OA.



Manager
Joined: 27 Oct 2013
Posts: 232
Location: India
Concentration: General Management, Technology
GMAT Date: 03022015
GPA: 3.88

Re: A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
25 Jan 2017, 03:56
Here we go,
I don't think that's a difficult question to someone who knows the formula to calculate Compound Interes and Simple Interest.
Compound Interest is calculated using 
A = P (1 + r/n)^(nt)  (1)
A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = the annual interest rate (decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for
and
Simple Interest is calculated using 
SI = (P x R x T)/100  (2)
Principal = P, Rate = R% per annum (p.a.) and Time = T years
Back to the question now.
A merchant invested $10,000 at 5% annual interest, compounded semiannually
Using equation 1
10000 * (1 + 0.05/2)^2 = 10506.25
Total interest earned in this case = 10506.25  10000 = 506.25  (a)
The question mentioned that tt the end of the first year, the total interest earned on each investment was the same..
Using equation (2)
506.25 = X * 0.05 * 1
so X = 10125
Option B should be the answer....
Now to answer to "im looking for a fast way to solve this."
I would have suggested to use the approximation technique by removing the decimal .25 in (a), but considering that the options are pretty close to each other, I don't think of any fast way to solve it as of now....



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
25 Jan 2017, 06:02
magniv123 wrote: A merchant invested $10,000 at 5% annual interest, compounded semiannually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X?
a. $10,000 b. $10,125 c. $10,250 d. $10,500 e. $10,825
im looking for a fast way to solve this.
thank you:) Welcome to the GMAT Club. Please read the following post before posting a question: rulesforpostingpleasereadthisbeforeposting133935.html Thank you.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Aug 2009
Posts: 6554

Re: hi can anyone help me with this difficult question?
[#permalink]
Show Tags
25 Jan 2017, 10:03
magniv123 wrote: A merchant invested $10,000 at 5% annual interest, compounded semiannually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X?
a. $10,000 b. $10,125 c. $10,250 d. $10,500 e. $10,825
im looking for a fast way to solve this.
thank you:) Hi, I can think of 2 ways.. 1) substitution.. Start from the middle value so that you can eliminate 2 choices either one on top or below.. Equation is \(10000(1+\frac{2.5}{100})^210000=\frac{10250*5}{100}\) 10000*1.025*1.02510000~500.. But 10250*.05~ 612.. So it has to be less than 10250.. AND ofcourse it has to be more than 10000 Only value left is 10125.. 2) method.. Leave 10000 and take it as 1.. So \((1+\frac{2.5}{100})^21=\frac{x*5}{100}\) 1.025*1.0251=x/20.......0.00506=x/20.....X=0.506*20=1.012.. Ans= 1.012*10000=10120 B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior Manager
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
GPA: 3

A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
16 Apr 2017, 00:20
chetan2u wrote: magniv123 wrote: A merchant invested $10,000 at 5% annual interest, compounded semiannually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X?
a. $10,000 b. $10,125 c. $10,250 d. $10,500 e. $10,825
im looking for a fast way to solve this.
thank you:) Hi, I can think of 2 ways.. 1) substitution.. Start from the middle value so that you can eliminate 2 choices either one on top or below.. Equation is \(10000(1+\frac{2.5}{100})^210000=\frac{10250*5}{100}\) 10000*1.025*1.02510000~500.. But 10250*.05~ 612.. So it has to be less than 10250.. AND ofcourse it has to be more than 10000 Only value left is 10125.. 2) method.. Leave 10000 and take it as 1.. So \((1+\frac{2.5}{100})^21=\frac{x*5}{100}\) 1.025*1.0251=x/20.......0.00506=x/20.....X=0.506*20=1.012.. Ans= 1.012*10000=10120 B I came up with another fast way.. Because the amount in the first case has been invested semiannually, we can divide it into two periods of 6 months each. In the first 6 months the interest earned will be = 250 In the next 6 months the interest will be = 250 + interest on 250 which is 250 + 25/4 Now this total interest earned is equal to 5% of X.. \(250 + 250 + \frac{25}{4} = \frac{5}{100}*X\) \(X = 10125\) (B) This method probably minimizes the calculations.
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 19 Feb 2015
Posts: 8

Re: A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
21 Apr 2017, 21:21
Bunuel wrote: magniv123 wrote: A merchant invested $10,000 at 5% annual interest, compounded semiannually, and an amount of $X at 5% simple annual interest. At the end of the first year, the total interest earned on each investment was the same. What is the value of X?
a. $10,000 b. $10,125 c. $10,250 d. $10,500 e. $10,825
im looking for a fast way to solve this.
thank you:) Hi Bunuel, Can we solve the prblm in the below way ? Total amount= 10000+5/100 * 10000 =10500 CI amount should be little greater than > 10500 So in order to equal to an amount little greater than 10500, the nearest amount on which SI is calculated will be little greater than 10000, which is 10125. Please let me know if this method can be used.



Intern
Joined: 26 Sep 2017
Posts: 14

Re: A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
28 Oct 2017, 07:49
DesiGmat wrote: Here we go,
I don't think that's a difficult question to someone who knows the formula to calculate Compound Interes and Simple Interest.
Compound Interest is calculated using 
A = P (1 + r/n)^(nt)  (1)
A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = the annual interest rate (decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for
and
Simple Interest is calculated using 
SI = (P x R x T)/100  (2)
Principal = P, Rate = R% per annum (p.a.) and Time = T years
Back to the question now.
A merchant invested $10,000 at 5% annual interest, compounded semiannually
Using equation 1
10000 * (1 + 0.05/2)^2 = 10506.25
Total interest earned in this case = 10506.25  10000 = 506.25  (a)
The question mentioned that tt the end of the first year, the total interest earned on each investment was the same..
Using equation (2)
506.25 = X * 0.05 * 1
so X = 10125
Option B should be the answer....
Now to answer to "im looking for a fast way to solve this."
I would have suggested to use the approximation technique by removing the decimal .25 in (a), but considering that the options are pretty close to each other, I don't think of any fast way to solve it as of now.... Hi! Could you clarify what am I doing wrong? I got following equation for 2nd case: x(1+0,05) = x+506,25 Why we shouldn't add investments ? Thank you



Retired Moderator
Joined: 28 May 2014
Posts: 528

Re: A merchant invested $10,000 at 5% annual interest, compounded semiann
[#permalink]
Show Tags
28 Oct 2017, 08:16
The merchant invested $10,000 at 5% annual interest, compounded semiannually So total interest earned from this investment: 10000 * (1 + 0.05/2)^2  10000 = 506.25 Now Suppose the principle for 2nd investment = x The interests earned are equal. Hence, x * 0.05 * 1 = 506.25 x = 506.25/0.05 = 10125 Ans: B.
_________________
440 to 730: If I Can, You Can Too




Re: A merchant invested $10,000 at 5% annual interest, compounded semiann &nbs
[#permalink]
28 Oct 2017, 08:16






