An investor opened a money market account with a single deposit of $60

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!

Nice one mate! Cheers!
JT

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

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?

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.

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.

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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%.

Hi kanigmat011 - the CI and SI are same till the first compounding (and not the first year), which in this case is 1st quarter. But the question asks for the rate of interest for the 4th quarter. Note that till the 4th quarter the principal for CI and SI would change. While the principal for SI would remain at 6000 the principal for CI would increase to 6400.

For the example which you took, if the CI is compounded semi-annually instead of annually, the interest for the first year for CI would be greater than that of SI. CI and SI would be equal for the first 6 months only i.e. till the first compounding.

Hope its clear. Let me know if you are having trouble at any point.

Regards
Harsh

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

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%

Total interest earned for the first three quarters is 400
therefore, he has to earn 200 in the fourth quarter in order to make up 10% on 6000
Since it is compounded, P=6400, t=1/4, r=?, interest =200
Apply simple interest formula
r=12.5%

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)

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

most logical answer

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