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Question Stats: 59% (02:42) correct 41% (02:39) wrong based on 118 sessions

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A merchant invested $10,000 at 5% annual interest, compounded semi-annually, and an amount of$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 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: 202 Location: India Concentration: General Management, Technology GMAT Date: 03-02-2015 GPA: 3.88 Re: A merchant invested$10,000 at 5% annual interest, compounded semi-ann  [#permalink]

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1
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 semi-annually 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 V Joined: 02 Sep 2009 Posts: 57191 Re: A merchant invested$10,000 at 5% annual interest, compounded semi-ann  [#permalink]

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magniv123 wrote:
A merchant invested $10,000 at 5% annual interest, compounded semi-annually, and an amount of$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: rules-for-posting-please-read-this-before-posting-133935.html Thank you. _________________ Math Expert V Joined: 02 Aug 2009 Posts: 7755 Re: hi can anyone help me with this difficult question? [#permalink] ### Show Tags magniv123 wrote: A merchant invested$10,000 at 5% annual interest, compounded semi-annually,
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 $$10000(1+\frac{2.5}{100})^2-10000=\frac{10250*5}{100}$$
10000*1.025*1.025-10000~500..
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 $$(1+\frac{2.5}{100})^2-1=\frac{x*5}{100}$$
1.025*1.025-1=x/20.......0.00506=x/20.....X=0.506*20=1.012..
Ans= 1.012*10000=10120

B
_________________
Senior Manager  G
Joined: 03 Apr 2013
Posts: 268
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41 GPA: 3
A merchant invested $10,000 at 5% annual interest, compounded semi-ann [#permalink] ### Show Tags 1 chetan2u wrote: magniv123 wrote: A merchant invested$10,000 at 5% annual interest, compounded semi-annually,
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 $$10000(1+\frac{2.5}{100})^2-10000=\frac{10250*5}{100}$$
10000*1.025*1.025-10000~500..
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 $$(1+\frac{2.5}{100})^2-1=\frac{x*5}{100}$$
1.025*1.025-1=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 semi-annually, 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  B
Joined: 19 Feb 2015
Posts: 8
Re: A merchant invested $10,000 at 5% annual interest, compounded semi-ann [#permalink] ### Show Tags Bunuel wrote: magniv123 wrote: A merchant invested$10,000 at 5% annual interest, compounded semi-annually,
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  B
Joined: 26 Sep 2017
Posts: 12
Re: A merchant invested $10,000 at 5% annual interest, compounded semi-ann [#permalink] ### Show Tags 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 semi-annually

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
Current Student V
Joined: 28 May 2014
Posts: 517
GMAT 1: 730 Q49 V41 Re: A merchant invested $10,000 at 5% annual interest, compounded semi-ann [#permalink] ### Show Tags The merchant invested$10,000 at 5% annual interest, compounded semi-annually

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.
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Non-Human User Joined: 09 Sep 2013
Posts: 12052
Re: A merchant invested $10,000 at 5% annual interest, compounded semi-ann [#permalink] ### Show Tags Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: A merchant invested$10,000 at 5% annual interest, compounded semi-ann   [#permalink] 05 Aug 2019, 21:15
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