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# If a $3,000 deposit is made into a savings account that pays 6 percent SORT BY: Tags: Show Tags Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 94302 Own Kudos [?]: 640182 [13] Given Kudos: 84576 GMAT Club Legend Joined: 18 Aug 2017 Status:You learn more from failure than from success. Posts: 7962 Own Kudos [?]: 4207 [0] Given Kudos: 243 Location: India Concentration: Sustainability, Marketing GMAT Focus 1: 545 Q79 V79 DI73 GPA: 4 WE:Marketing (Energy and Utilities) Senior Manager Joined: 18 Jun 2018 Posts: 334 Own Kudos [?]: 200 [4] Given Kudos: 1283 Concentration: Finance, Healthcare VP Joined: 09 Mar 2016 Posts: 1143 Own Kudos [?]: 1024 [0] Given Kudos: 3851 Re: If a$3,000 deposit is made into a savings account that pays 6 percent [#permalink]
funsogu wrote:
Archit3110 You have an error in your equation. You have to divide r% by number of times the interested will be compounded, 12 in this case. Correct answer is C.

Amount = P(1+r%/n)^nt = $3,000(1+0.06/1200)^12 =$3000(1.005)^12 ~ $3,185 You could also have assumed taken this as a simple interest question to get$3,180. Answer will be a little bit more than this number since we are dealing with compound interest. So best answer is $3,185. Archit3110 wrote: If a$3,000 deposit is made into a savings account that pays 6 percent interest, compounded monthly, and there are no other deposits or withdrawals from the account, how much money, rounded to the nearest dollar, is in the account at the end of one year?

A. $2,160 B.$3,180
C. $3,185 D.$5,160
E. $6,037 CI=P(1+r%)^t = 3000(1.06)^12 = ~6036.5 = option E hi there funsogu have one question: $$3000(1.062)^12$$ how to calculate it without calculator (i mean when it is raised to 12th power) ;? any idea? VP Joined: 09 Mar 2016 Posts: 1143 Own Kudos [?]: 1024 [1] Given Kudos: 3851 Re: If a$3,000 deposit is made into a savings account that pays 6 percent [#permalink]
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hi there funsogu have one question:

$$3000(1.062)^{12}$$ how to calculate it without calculator (i mean when it is raised to 12th power) ;? any idea?[/quote]
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If a $3,000 deposit is made into a savings account that pays 6 percent [#permalink] 2 Kudos 2 Bookmarks Hi dave13. I am not an expert but sure I can help. Firstly, what you are trying to determine is 3,000(1.005)^12 not 3,000(1.062)^12 . I was at a dilemma on how to solve this without calculator so I decided to just use simple interest and choose an answer that is slightly above the answer for simple interest ($3,180) and chose C since it is the closest. I then googled "how to solve compound interest rate questions fast" and came across this article (https://gmat.economist.com/gmat-advice/ ... ners-guide) by the theeconomist. Turned out they have the same approach. Hope it helps. Cheers!

dave13 wrote:
hi there funsogu have one question:

$$3000(1.062)^{12}$$ how to calculate it without calculator (i mean when it is raised to 12th power) ;? any idea?
[/quote]
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Re: If a $3,000 deposit is made into a savings account that pays 6 percent [#permalink] Expert Reply Bunuel wrote: If a$3,000 deposit is made into a savings account that pays 6 percent interest, compounded monthly, and there are no other deposits or withdrawals from the account, how much money, rounded to the nearest dollar, is in the account at the end of one year?

A. $2,160 B.$3,180
C. $3,185 D.$5,160
E. $6,037 Solution: We use the compound interest formula A = P(1 + r/n)^nt, where A is the ending amount, P is the starting amount (P =$3,000), r is the interest rate (r = 0.06), n is the number of times the interest is compounded per year (n = 12), and t is the number of years (t = 1).

The amount of money in the account, rounded to the nearest dollar, at the end of one year is:

A = 3000(1 + 0.06/12)^12 = 3000(1.005)^12 = $3,185 Answer: C VP Joined: 10 Jul 2019 Posts: 1385 Own Kudos [?]: 576 [1] Given Kudos: 1656 If a$3,000 deposit is made into a savings account that pays 6 percent [#permalink]
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6% Compounded monthly for 1 year -----> 6% / 12 =

.05% Interest Compounded for each of the 12 months in the years (12 times)

Amount = $3,000 * (100% + .05%)^12 The Amount of Interest earned in month 1 =$3,000 * .05% = $3,000 * (1/200) =$15

In Month 2 , the Amount of Interest earned on the Interest from Month 1 will ONLY be ---> .05% * $15 From an approximation, we can see that the amount of Compound Interest earned on Interest will NOT be that much Greater than the Amount earned on Simple Interest Thus, if we Calculate the amount that the Investment would have earned at SIMPLE INTEREST ----> we can Estimate and say that the Amount earned at COMPOUND Interest will be SLIGHTLY MORE than the amount earned at Simple Interest$3,000 * (.05%) = $15 At Simple Interest earned at the End of Each month for 12 months ----->$15 * (12) = $180 = Total Simple Interest earned Amount that would have been earned at Simple Interest =$3,000 + $180 =$3,180

The Actual Answer should be SLIGHTLY LARGER > $3,180 -C- fits perfectly$3, 185
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Re: If a $3,000 deposit is made into a savings account that pays 6 percent [#permalink] 1 Bookmarks Expert Reply Let us set up the equation required to calculate the amount. When compounding is done monthly, Amount is calculated using the equation, A = P $$(1 + \frac{R }{ 1200}) ^ {12T}$$, Where P = Principal, R = Rate of Interest (in percent) and T = Period (in years) In this question, P = 3000, R = 6 and T = 1 Substituting the values, we have, A = 3000 $$( 1 + \frac{6 }{ 1200} ) ^ {12}$$ Simplifying, we have, A = 3000 $$( 1 + \frac{1 }{ 200}) ^{12}$$ or A = 3000 $$( 1.005) ^{12}$$. The obvious question that a lot of us will have on our minds will be, “How do I evaluate the exponent without a calculator?”. That is probably where GMAT does not expect you to be a number cruncher, but more of a smart estimator. Now, 0.005 = ½ percent. ½ percent of 3000 would be 15; so, after 1 month, the amount would be 3015$.

Now, ½ percent of 15 = 0.0075, a very small value.

So, if we estimate that we would get a very small value above $15, for each of the 12 months, we wouldn’t be wrong at all. Therefore, total interest in 12 months = 15 * 12 = 180. So, is the amount 3180? NO. Remember that there is a small value over and above 15 in the interest component of every month after the 2nd month. Therefore, we need a value slightly above 3180, that would be 3185. Answer option A is non-sensical. Answer options D and E are impossible to reach in one year considering the meager rate at which interest is being paid out. The correct answer option is C. Intern Joined: 12 Apr 2021 Posts: 13 Own Kudos [?]: 1 [1] Given Kudos: 32 Re: If a$3,000 deposit is made into a savings account that pays 6 percent [#permalink]
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Bunuel wrote:
If a $3,000 deposit is made into a savings account that pays 6 percent interest, compounded monthly, and there are no other deposits or withdrawals from the account, how much money, rounded to the nearest dollar, is in the account at the end of one year? A.$2,160
B. $3,180 C.$3,185
D. $5,160 E.$6,037

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Isn't the question supposed to specify whether the interest rate is annual or quaterly or monthly??
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Re: If a $3,000 deposit is made into a savings account that pays 6 percent [#permalink] 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: If a$3,000 deposit is made into a savings account that pays 6 percent [#permalink]
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