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

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Math Expert
Joined: 02 Sep 2009
Posts: 51227
How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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17 Jan 2017, 09:04
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:05) correct 47% (02:05) wrong based on 171 sessions

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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

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Joined: 05 Mar 2015
Posts: 1004
How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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17 Jan 2017, 09:45
1
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
Intern
Joined: 06 Oct 2017
Posts: 3
Location: United States (TX)
GMAT 1: 580 Q32 V37
GPA: 3.31
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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23 Oct 2017, 17:45
I am confused on the solution formula used. Could someone break it down more in detail?
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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23 Oct 2017, 23:17
2
1
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.

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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51227
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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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.

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.

4. Percents and Iterest

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
_________________
Intern
Joined: 06 Oct 2017
Posts: 3
Location: United States (TX)
GMAT 1: 580 Q32 V37
GPA: 3.31
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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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.

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.

4. Percents and Iterest

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.

Thanks Bunuel!
Manager
Joined: 31 Jan 2018
Posts: 70
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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12 May 2018, 04:58
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

Let the amount invested is A

since it is compounded semi annually, the rate of interest will be 10/2 = 5% and the time will be 1 * 2 = 2

According to question:

A (1 + 5/100)^2 - A = 51.25

A(441/400) - A = 51.25
--> 41A/400 = 51.25
==> 41A = 20500
therefore A(Amount invested) = 20500/41 = 500
Manager
Joined: 17 Jan 2017
Posts: 61
Re: How much money must be invested at 10% annual interest, compounded sem  [#permalink]

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12 May 2018, 09:00
If the interest is compounded anually answer D were correct.
The answer has to be very close to D though.
Re: How much money must be invested at 10% annual interest, compounded sem &nbs [#permalink] 12 May 2018, 09:00
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