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If Joanie puts $500 in a savings account that earns 10 percent annual

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If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 09 Sep 2015, 00:03
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:07) correct 21% (01:20) wrong based on 116 sessions

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If Joanie puts $500 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?

A) $51.25
B) $510
C) $550
D) $551.25
E) $565


Kudos for a correct solution.

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Re: If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 09 Sep 2015, 01:04
Bunuel wrote:
If Joanie puts $500 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?

A) $51.25
B) $510
C) $550
D) $551.25
E) $565


Kudos for a correct solution.


Since, money is compounded semianually, rate of interest=10/2=5% and time =1*2=2
C.I=(5%of $500)+5%of(5%of $500)=$51.25
Amount=$500+51.25=$551.25
Answer D
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Re: If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 09 Sep 2015, 01:42
Solution :

\(Amount = 500[1+\frac{5}{100}]^{2} = 500*(1.05)*(1.05) = 551.25\)

Option, D
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Re: If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 09 Sep 2015, 02:21
yep. D is correct choice
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Re: If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 13 Sep 2015, 07:47
Bunuel wrote:
If Joanie puts $500 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?

A) $51.25
B) $510
C) $550
D) $551.25
E) $565


Kudos for a correct solution.


PRINCETON REVIEW OFFICIAL SOLUTION:

Principal + compound interest = \(500*(1+.05)^2\)

But there’s an even easier way. On the GMAT, compound interest is going to be just a little more than simple interest. So let’s first think about simple interest. 10% of 500 is 50, so simple interest would be $50 and the account would contain $550. With compound interest it will earn just a little bit more than that, so the answer must be D.

This might be surprising to you, because compound interest is often described as a very powerful force, something that can turn small sums into great fortunes. However this is only true over long time horizons. Over a period of decades, compound interest can have a very powerful effect: 50 years of 10% annual simple interest in the problem above would only increase the value of the account to $3000. But 50 years of 10% annual interest compounded semiannually would increase the value of the account to more than $65,000.

However, as mentioned, over the very short term compound interest has a negligible effect and adds only a tiny bit to simple interest. So this means that for most compound interest problems, you can just ballpark an answer rather than calculating with the formula. Given this, you may wonder if it’s worth knowing the formula at all!

One reason you might want to be familiar with the formula anyway is that the GMAT has in the past presented questions on which the answer choices weren’t amounts of money, but rather formulas. The question asked you to pick the formula that represented the correct amount of money. Although you could solve a question like that by plugging the values in the problem into the answer choices and ballparking, the easiest thing would be to know the formula and simply pick it out of the available options.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If Joanie puts $500 in a savings account that earns 10 percent annual  [#permalink]

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New post 30 Oct 2018, 08:29
Bunuel wrote:
Bunuel wrote:
If Joanie puts $500 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?

A) $51.25
B) $510
C) $550
D) $551.25
E) $565


Kudos for a correct solution.


PRINCETON REVIEW OFFICIAL SOLUTION:

Principal + compound interest = \(500*(1+.05)^2\)





But there’s an even easier way. On the GMAT, compound interest is going to be just a little more than simple interest. So let’s first think about simple interest. 10% of 500 is 50, so simple interest would be $50 and the account would contain $550. With compound interest it will earn just a little bit more than that, so the answer must be D.

This might be surprising to you, because compound interest is often described as a very powerful force, something that can turn small sums into great fortunes. However this is only true over long time horizons. Over a period of decades, compound interest can have a very powerful effect: 50 years of 10% annual simple interest in the problem above would only increase the value of the account to $3000. But 50 years of 10% annual interest compounded semiannually would increase the value of the account to more than $65,000.

However, as mentioned, over the very short term compound interest has a negligible effect and adds only a tiny bit to simple interest. So this means that for most compound interest problems, you can just ballpark an answer rather than calculating with the formula. Given this, you may wonder if it’s worth knowing the formula at all!

One reason you might want to be familiar with the formula anyway is that the GMAT has in the past presented questions on which the answer choices weren’t amounts of money, but rather formulas. The question asked you to pick the formula that represented the correct amount of money. Although you could solve a question like that by plugging the values in the problem into the answer choices and ballparking, the easiest thing would be to know the formula and simply pick it out of the available options.




IMO
If Joanie puts $500 in a savings account that earns 10 percent annual interest
compounded semiannually, how much money will be in the account after one year?
500*10/100*1/2=25>>500+25=525*10/100*1/2=26.25>>525+26.25=551.25
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Re: If Joanie puts $500 in a savings account that earns 10 percent annual &nbs [#permalink] 30 Oct 2018, 08:29
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