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How much money must be invested at 10% annual interest, compounded sem

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How much money must be invested at 10% annual interest, compounded sem [#permalink]

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How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00
[Reveal] Spoiler: OA

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How much money must be invested at 10% annual interest, compounded sem [#permalink]

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New post 17 Jan 2017, 09:45
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Bunuel wrote:
How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00

Algebraic approach
CI=P*(1+r/100)^t
CI=P+51.25
thus P+51.25=P(1+10/(2*100)^2
P=500

2nd logical approach

10% of 500 =50
thus total profit is a bit more since interest earned compounded basis
thus profit must be 51.25
(check for first year 500+25=525
second year 525*5/100=26.25
total 525+26.25= 551.25)

Thus Ans C

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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink]

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New post 23 Oct 2017, 17:45
I am confused on the solution formula used. Could someone break it down more in detail?

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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink]

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New post 23 Oct 2017, 23:17
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Expert's post
twash017 wrote:
I am confused on the solution formula used. Could someone break it down more in detail?


How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00

10% annual interest, compounded semi-annually means that the investment earns 5% in every 6 months.

So, we are looking for such x, which satisfies: x*1.05^2 = x + 51.25

0.1025x = 51.25;
1025x = 512500;
x = 500.

Answer: C.

Another way: since 10% annual interest is compounded semi-annually, then the actual interest will be a little bit more that 10% (because of the interest earned on interest). Thus, $51.25 of interest must be a little bit more that 10% of the correct answer. Only C fits.

Answer: C.
_________________

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

Kudos [?]: 135613 [2], given: 12705

Expert Post
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink]

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New post 23 Oct 2017, 23:18
Bunuel wrote:
twash017 wrote:
I am confused on the solution formula used. Could someone break it down more in detail?


How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00

10% annual interest, compounded semi-annually means that the investment earns 5% in every 6 months.

So, we are looking for such x, which satisfies: x*1.05^2 = x + 51.25

0.1025x = 51.25;
1025x = 512500;
x = 500.

Answer: C.

Another way: since 10% annual interest is compounded semi-annually, then the actual interest will be a little bit more that 10% (because of the interest earned on interest). Thus, $51.25 of interest must be a little bit more that 10% of the correct answer. Only C fits.

Answer: C.


4. Percents and Iterest



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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

Kudos [?]: 135613 [0], given: 12705

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Joined: 06 Oct 2017
Posts: 3

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Location: United States (TX)
GMAT 1: 550 Q31 V35
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink]

Show Tags

New post 24 Oct 2017, 13:09
Bunuel wrote:
Bunuel wrote:
twash017 wrote:
I am confused on the solution formula used. Could someone break it down more in detail?


How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?

A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00

10% annual interest, compounded semi-annually means that the investment earns 5% in every 6 months.

So, we are looking for such x, which satisfies: x*1.05^2 = x + 51.25

0.1025x = 51.25;
1025x = 512500;
x = 500.

Answer: C.

Another way: since 10% annual interest is compounded semi-annually, then the actual interest will be a little bit more that 10% (because of the interest earned on interest). Thus, $51.25 of interest must be a little bit more that 10% of the correct answer. Only C fits.

Answer: C.


4. Percents and Iterest



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.



Thanks Bunuel!

Kudos [?]: 0 [0], given: 22

Re: How much money must be invested at 10% annual interest, compounded sem   [#permalink] 24 Oct 2017, 13:09
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