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29 Dec 2009, 13:28
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Question Stats:

42% (02:43) correct 58% (02:51) wrong based on 445 sessions

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An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was$125, $130, and$145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A. 3.1%
B. 9.3%
C. 10.0%
D. 10.5%
E. 12.5%
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Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 29 Dec 2009, 13:53 29 1 15 I'm not sure this method dodges formulas as much as you want, but here goes: 10% of the initial deposit is$600, and the account has already earned $125+$130+$145 =$400. Must make $200 in the last quarter, and the balance at that point is$6000+$400 =$6400.

This method is called Benchmarking:
If 1% (annual rate) were earned on $6400, that would be$64 a year or $64/4 =$16 per quarter.

How many $16 payments (i.e. 1 percent payments) must this account earn to collect$200? $200/$16 = 12.5 of the 1% payments, or 12.5%.

### Show Tags

04 Mar 2010, 22:13
15
1
cccmom wrote:
I sure would appreciate some help on this one. If I don't know the formula, how can I solve conceptually?

An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was$125, $130, and$145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A - 3.1%
B - 9.3%
C - 10.0%
D - 10.5%
E - 12.5%

We know 10% of 6000 is 600
already earned is Rs. 400 in 3 quarters
balance to be earned is 200 on amount of 6400 (6000+400 intt)

we get quarterly Rate of Interest as 3.125% (200/6400).

anually it would be 3.125*4 = 12.5%

hope that works out for you.

Award KUDOS if you appreciate !!!
Manager
Joined: 22 Dec 2009
Posts: 234
Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 01 Jan 2010, 11:52 1 esledge wrote: I'm not sure this method dodges formulas as much as you want, but here goes: 10% of the initial deposit is$600, and the account has already earned $125+$130+$145 =$400. Must make $200 in the last quarter, and the balance at that point is$6000+$400 =$6400.

This method is called Benchmarking:
If 1% (annual rate) were earned on $6400, that would be$64 a year or $64/4 =$16 per quarter.

How many $16 payments (i.e. 1 percent payments) must this account earn to collect$200? $200/$16 = 12.5 of the 1% payments, or 12.5%.

Alternatively, you could benchmark using 10% (annual rate). That would give us $640 a year or$160 per quarter (not enough, but A,B, and C are wrong for sure). $160 plus$40 (or 1/4 of $160) is what we need. Thus, 10% + (1/4)(10%) = 12.5% Nice one mate! Cheers! JT e-GMAT Representative Joined: 04 Jan 2015 Posts: 3230 Re: An investor opened a money market account with a single deposit of$60  [#permalink]

### Show Tags

20 Apr 2015, 04:06
1
1
kanigmat011 wrote:
esledge wrote:
I'm not sure this method dodges formulas as much as you want, but here goes:

10% of the initial deposit is $600, and the account has already earned$125+$130+$145 = $400. Must make$200 in the last quarter, and the balance at that point is $6000+$400 = $6400. This method is called Benchmarking: If 1% (annual rate) were earned on$6400, that would be $64 a year or$64/4 = $16 per quarter. How many$16 payments (i.e. 1 percent payments) must this account earn to collect $200?$200/$16 = 12.5 of the 1% payments, or 12.5%. Alternatively, you could benchmark using 10% (annual rate). That would give us$640 a year or $160 per quarter (not enough, but A,B, and C are wrong for sure).$160 plus $40 (or 1/4 of$160) is what we need. Thus, 10% + (1/4)(10%) = 12.5%

''

Hi Esledge

Thanks for wonderful explanation,but i have a confusion here.
If we use the normal interest computation formula Interest=( Amount *Rate of Interest *Duration)/100
We get( 6000*R*0.25)/100=125
R=8.3
Can you through some light why this technique is not applicable here?

Hi kanigmat011 that will not applicable because you are using the formula for Simple Interest calculation where as the question asks for Compound Interest working. Now, how do we know that the question deals with CI? Because the interest earned on the account was reinvested quarterly; thus the interest earned during the previous quarters will also further earn interest on them.

In case of Simple Interest, the interest earned during the previous quarters do not earn interest on them, only the principal does. Hence, the technique you are using would not apply here.

The other way to solve this problem would be:

Amount of interest to be earned in the last quarter= 6000* 0.10 - (125+130+145) = 200
Principal balance in the account = 6000 + 400 = 6400

Hence, quarterly interest rate = $$\frac{200}{6400}$$ * 100 = 3.125%

So, the annual interest rate = 3.125% * 4 = 12.5%

Hope it helps!

Regards
Harsh
_________________
Intern
Joined: 15 Feb 2015
Posts: 5
An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 12 Aug 2015, 02:25 1 This can be simply done with a clear understanding of compound interest.In compound interest too, you reinvest the interest earned. Basically, CI1+CI2+CI3 = 125 +130 +145 = 400 So by the end of 3 quarters, total amount would be 6400$
i.e, 6000(1+r/100)^3 = 6400 ----(1)
By the end of 4th quarters, the interest should be 10% of the amount initially invested, which is 10% of 6000 = 600
i.e, 6000(1+r/100)^4 =6600 ----(2)

Divide eqn (1) and (2), you will get quarterly r of 3.125%
=> Annual rate would be 3.125 * 4 = 12.5%
Manager
Joined: 10 Jun 2015
Posts: 110

### Show Tags

23 Dec 2015, 02:28
1
mustdoit wrote:
cccmom wrote:
I sure would appreciate some help on this one. If I don't know the formula, how can I solve conceptually?

An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was$125, $130, and$145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A - 3.1%
B - 9.3%
C - 10.0%
D - 10.5%
E - 12.5%

We know 10% of 6000 is 600
already earned is Rs. 400 in 3 quarters
balance to be earned is 200 on amount of 6400 (6000+400 intt)

we get quarterly Rate of Interest as 3.125% (200/6400).

anually it would be 3.125*4 = 12.5%

hope that works out for you.

Award KUDOS if you appreciate !!!

Intern
Joined: 07 Dec 2009
Posts: 11

### Show Tags

12 Apr 2015, 04:06
mustdoit wrote:
cccmom wrote:
I sure would appreciate some help on this one. If I don't know the formula, how can I solve conceptually?

An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was$125, $130, and$145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A - 3.1%
B - 9.3%
C - 10.0%
D - 10.5%
E - 12.5%

We know 10% of 6000 is 600
already earned is Rs. 400 in 3 quarters
balance to be earned is 200 on amount of 6400 (6000+400 intt)

we get quarterly Rate of Interest as 3.125% (200/6400).

anually it would be 3.125*4 = 12.5%

hope that works out for you.

Award KUDOS if you appreciate !!!

I am not able to get the last line.why we are multiplying 3.125*4?
Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 105
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

### Show Tags

12 Apr 2015, 10:50
You need to earn $200 in the last Q to earn 10% for the year. the total money at the end of Q3 is 6400. $$\frac{200}{6400}$$is approximately 3.xx% for the Q, multiply that by 4, you will see the answer is 12.xxx. Only one choice. Senior Manager Joined: 28 Feb 2014 Posts: 289 Location: United States Concentration: Strategy, General Management Re: An investor opened a money market account with a single deposit of$60  [#permalink]

### Show Tags

12 Apr 2015, 16:42
ssriva2 wrote:
mustdoit wrote:
cccmom wrote:
I sure would appreciate some help on this one. If I don't know the formula, how can I solve conceptually?

An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was$125, $130, and$145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A - 3.1%
B - 9.3%
C - 10.0%
D - 10.5%
E - 12.5%

We know 10% of 6000 is 600
already earned is Rs. 400 in 3 quarters
balance to be earned is 200 on amount of 6400 (6000+400 intt)

we get quarterly Rate of Interest as 3.125% (200/6400).

anually it would be 3.125*4 = 12.5%

hope that works out for you.

Award KUDOS if you appreciate !!!

I am not able to get the last line.why we are multiplying 3.125*4?

I believe it is because the question asks for the "annual rate" of interest.

Hence we have to do a conversion from quarterly to annual.
Manager
Joined: 27 Jul 2014
Posts: 232
Schools: ISB '15
GMAT 1: 660 Q49 V30
GPA: 3.76
Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 20 Apr 2015, 03:32 esledge wrote: I'm not sure this method dodges formulas as much as you want, but here goes: 10% of the initial deposit is$600, and the account has already earned $125+$130+$145 =$400. Must make $200 in the last quarter, and the balance at that point is$6000+$400 =$6400.

This method is called Benchmarking:
If 1% (annual rate) were earned on $6400, that would be$64 a year or $64/4 =$16 per quarter.

How many $16 payments (i.e. 1 percent payments) must this account earn to collect$200? $200/$16 = 12.5 of the 1% payments, or 12.5%.

Alternatively, you could benchmark using 10% (annual rate). That would give us $640 a year or$160 per quarter (not enough, but A,B, and C are wrong for sure). $160 plus$40 (or 1/4 of $160) is what we need. Thus, 10% + (1/4)(10%) = 12.5% '' Hi Esledge Thanks for wonderful explanation,but i have a confusion here. If we use the normal interest computation formula Interest=( Amount *Rate of Interest *Duration)/100 We get( 6000*R*0.25)/100=125 R=8.3 Can you through some light why this technique is not applicable here? Manager Joined: 27 Jul 2014 Posts: 232 Schools: ISB '15 GMAT 1: 660 Q49 V30 GPA: 3.76 Re: An investor opened a money market account with a single deposit of$60  [#permalink]

### Show Tags

20 Apr 2015, 10:10
EgmatQuantExpert wrote:
kanigmat011 wrote:
esledge wrote:
I'm not sure this method dodges formulas as much as you want, but here goes:

10% of the initial deposit is $600, and the account has already earned$125+$130+$145 = $400. Must make$200 in the last quarter, and the balance at that point is $6000+$400 = $6400. This method is called Benchmarking: If 1% (annual rate) were earned on$6400, that would be $64 a year or$64/4 = $16 per quarter. How many$16 payments (i.e. 1 percent payments) must this account earn to collect $200?$200/$16 = 12.5 of the 1% payments, or 12.5%. Alternatively, you could benchmark using 10% (annual rate). That would give us$640 a year or $160 per quarter (not enough, but A,B, and C are wrong for sure).$160 plus $40 (or 1/4 of$160) is what we need. Thus, 10% + (1/4)(10%) = 12.5%

''

Hi Esledge

Thanks for wonderful explanation,but i have a confusion here.
If we use the normal interest computation formula Interest=( Amount *Rate of Interest *Duration)/100
We get( 6000*R*0.25)/100=125
R=8.3
Can you through some light why this technique is not applicable here?

Hi kanigmat011 that will not applicable because you are using the formula for Simple Interest calculation where as the question asks for Compound Interest working. Now, how do we know that the question deals with CI? Because the interest earned on the account was reinvested quarterly; thus the interest earned during the previous quarters will also further earn interest on them.

In case of Simple Interest, the interest earned during the previous quarters do not earn interest on them, only the principal does. Hence, the technique you are using would not apply here.

The other way to solve this problem would be:

Amount of interest to be earned in the last quarter= 6000* 0.10 - (125+130+145) = 200
Principal balance in the account = 6000 + 400 = 6400

Hence, quarterly interest rate = $$\frac{200}{6400}$$ * 100 = 3.125%

So, the annual interest rate = 3.125% * 4 = 12.5%

Hope it helps!

Regards
Harsh

Thanks Harsh
But as per my understanding SI or CI for first initial year is same.
for Eg R=10% amount =1000 and amount is invested in SI and CI for next 2 years
so for 1st year SI=1000*10*1)/100=100
CI for 1st year= 1000(1+10/100) which gives CI=100

So here in this case 1st quarter CI on amount of 6000 should be same as SI on amount of 6000 . So equating that we get rate of interest as
( 6000*R*0.25)/100=125
R= 8.33%.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3230

### Show Tags

01 Jul 2015, 21:16
Can anyone tell me whether my approach is correct?

6000(1+r/4)=125
6000(1+r/4)^2=130 [We take the previous value and multiply by (1+r/4) to express the reinvestment of the interest]
6000(1+r/4)^3=145
6000(1+r/4)^3(1+x/4)=600
145(1+x/4)=600

x approx = 12.55

E
Manager
Joined: 10 Jun 2015
Posts: 110

### Show Tags

04 Nov 2015, 16:51
If we are pressed for time, this is a way to make an educated guess.

After the 1 minute mark, I simply looked at the answer choices knowing that they may give us a monthly rate to trip us up. 3.1 x 4 ~12.5

So I went with 12.5
Manager
Joined: 14 Oct 2012
Posts: 157
An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags Updated on: 22 Apr 2017, 09:40 1 Hello Friends, i did this and got right answer: Step1: Simple interest to calculate amount at the end of 1st year: (P*r*T/100) 6000*10/100*1 = 600 Thus, total amount at the end of 1st year would be 6600. Step 2: Calculating rate of interest in Q4: Initially invested: 6000 Quarterly gains Q1:125, Q2:130 & Q3:145 Total gains = 400 Therefore principle at the beginning of 4th quarter: 6400 Time in the year = Q4 = 3 months = t = 3/12 = 1/4 compounded quarterly = n = 4. Formula: Balance = Principle*(1+r/n)^(t*n) We need to get 6600 by the end of 4th quarter. 6400*(1+r/100*1/4)^(1/4*4) = 6600 6400*(1+r/100*1/4) = 6600 6400 + 6400*(r/100)*(1/4) = 6600 6400*(r/100)*(1/4) = 200 64*(r/100)*(1/4) = 2 16*(r/100) = 2 r = (2/16)*100 = (1/8)*100 = 12.5% We need to remember that for the 1st compounding SI = CI and here it would be same for final quarter. (Better explained by Harsh e-gmat). Please critique my solution and let me know if you see anything wrong. Thanks Originally posted by manishtank1988 on 12 Aug 2016, 22:06. Last edited by manishtank1988 on 22 Apr 2017, 09:40, edited 1 time in total. An investor opened a money market account with a single deposit of$60   [#permalink] 12 Aug 2016, 22:06

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