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# GmatScore: Interest

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Manager
Joined: 20 Aug 2009
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28 Aug 2009, 04:02
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Question Stats:

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How much interest will $2400 earn at an annual rate f 8% in one year if interest is compounded every four months? a. 141 b. 150 c. 197 d. 234 e. 312 OA [Reveal] Spoiler: C Please explain. Manager Joined: 18 Jul 2009 Posts: 169 Location: India Schools: South Asian B-schools Followers: 2 Kudos [?]: 98 [0], given: 37 Re: GmatScore: Interest [#permalink] ### Show Tags 28 Aug 2009, 05:06 this is formula based sum...use compound interest formula only add interval to this formula for compounding interval is generally 1 as annually compounded....but here it is compounded 4 months in year that is 3 times a year hence interval (i) = 3 no of years = 1 A = P (1+(r/100))^n.....where r = 8/i & n = i*no of years A = 2400*((1+(8/300))^3) = 2597.16 ......Then Interest = A -P........2597.16 - 2400 = 197.16 =$ 197
Hence OA C
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Bhushan S.
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Manager
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29 Aug 2009, 05:44
C.I = P*(1 + r/n)^nT

Here, P = Principle amount = 2400
r = rate of interest in % = 8%
n = number of times the interest is compounded = 12/4 = 3
T = Time duration = 1 year

= 2400*(1 + 8/(100*3))^3*1
= 2400*(1.082)
= 2400 (1 + 0.082)

C.I formula gives the total amount with interest.

So interest earned = C.I - P = 2400 (1 + 0.082) - 2400
= 2400*0.082
= 196.8

Senior Manager
Joined: 30 Nov 2008
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14 Sep 2009, 11:50
Here is one other way of calculating CI to make calculations within 2 min timeframe. (In layman terms, CI is nothing but interest on the interest.) Based on this concept here is my approach -

Principle = 2400
Rate = 8%
Compounded every 4 months. (ie in a year, interest is calculated 3 times)

Apply CI forumula thrice but every time, you calculate SI, new principle = principle + Interest.

Step 1 First term CI = 2400 + 2400 * 0.08/3 = 2400 + 64
Step 2 Second term CI = 2464 + 2464 * 0.08/3 = 2464 + 65.44
Ste 3 Third Term = 2529.44 + 2529.44 * 0.08/3 = 2529.44 + 67.45

So the CI interest paid = 64 + 65.44 + 67.45 = 196.89 close to 197.
Senior Manager
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14 Sep 2009, 15:08
When I looked at the question I forgot the CI formula but you can approximate the answer pretty accurately.
The first 4 month cycle gives you
$2400 x 8/100 x 1/3 =$64

So you know immediately that 3 x 64 is the minimum which is $192. The additional compound interest on top of$64 for each cycle is going to be pretty small (around \$64 x 8/100 x 1/3)
Looking at the answer choices only C fits.
Manager
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06 Oct 2009, 12:51
Hey guys, I'm having a hard time coming up with a quicker way to figure out the Compound Interest problems within the 2 minutes mark.

For this particular question, yes you can use the simple interest version three times and you can get an answer fairly quickly, but when questions become much more complex, i doubt i'm going to be able to work out a quarterly interest for double digit years, all within 2 mins.

Heres the situation via the CI formula way and help me where I'm muddling or complicated it too much:

CI Formula states:
$$2400(1+ \frac{.08}{3})^3^(^1^)$$

Then, according to PEMDAS, you do the inside parenthesis first. So:
Step 1:$$\frac{.08}{3}= .02666666666$$ OR $$.0267$$
S2: $$1+.0267=1.0267$$
S3: $$1.0267^3$$ ? Am I seriously expected to do a 5 digit multiplication 4 times? And still finish within the 2 mins?
regardless here we go:
1.027
x1.027
7189
20540
+1027000
1.054729
x1.027
7383103
21054580
+1054729000
1.083166683
after that, it's pretty simple, but come on, theres got to be an easier way of doing this. the multiplication while easy, is super prone to mistakes, and thus takes in itself, 3ish mins. i say again, there's got to be an easier way.

fractions? still the same thing:

$$1+\frac{8}{300}$$
$$\frac{308}{300}^3$$

here we go again:
308
x308
2464
+110400
112864
x308
902892
+33859200
34762092

then the denominator is easy= 27000000

so now i have to quickly reduce $$\frac{34762092}{27000000}$$ ?
Come on you've got to be kidding me. just finding the reduction itself, will again, be very prone to mistakes, and could easily take over 3 mins.

can any of you guys help me out with figuring out where I'm going wrong here? is there a shortcut i'm not aware of? is there an estimating method that I dont' know?
Re: GmatScore: Interest   [#permalink] 06 Oct 2009, 12:51
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