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61 00:00

Difficulty:   95% (hard)

Question Stats: 43% (02:44) correct 57% (02:50) wrong based on 435 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%
Manhattan Prep Instructor Joined: 28 Aug 2009
Posts: 145
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 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

Esledge,

I gave you kudos! This is exactly what I was looking for! Thanks for the shortcuts and tips! You rock! Congrats also on your 790 score!
Manager  Joined: 22 Dec 2009
Posts: 242
Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 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 Manager  Joined: 18 Feb 2010 Posts: 126 Schools: ISB Re: An investor opened a money market account with a single deposit of$60  [#permalink]

### Show Tags

14
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 Aug 2014
Posts: 134

### Show Tags

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%

Because of the highlighted line shown below:

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 whatannual 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?
Intern  Joined: 24 Oct 2014
Posts: 39
Location: United States
GMAT 1: 710 Q49 V38 GMAT 2: 760 Q48 V47 Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 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  B
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management

### Show Tags

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?
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 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 _________________ Manager  B Joined: 27 Jul 2014 Posts: 234 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

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 V
Joined: 04 Jan 2015
Posts: 3158

### Show Tags

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
Intern  B
Joined: 15 Feb 2015
Posts: 5
An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 1 This can be simply done with a clear understanding of compound interest.In compound interest too, you reinvest the interest earned. Basically, CI1+CI2+CI3 = 125 +130 +145 = 400 So by the end of 3 quarters, total amount would be 6400$
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

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TooLong150 wrote:
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

First, theory
Amount = Principal+Interest
CI = PR^n-P

Secondly, the quarterly interests are not exact figures. It seems to be rounded off.
That could be the reason you did not get the accurate answer. You can look at my solution (matvan)
Manager  Joined: 23 Sep 2015
Posts: 79
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38 GPA: 3.5

### Show Tags

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 !!!

Manager  G
Joined: 14 Oct 2012
Posts: 158
An investor opened a money market account with a single deposit of $60 [#permalink] ### Show Tags 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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