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

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Bunuel
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How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   17 Jan 2017, 10:04
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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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Bunuel
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   24 Oct 2017, 00:17
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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.
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rohit8865
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How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   17 Jan 2017, 10:45
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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] New post   23 Oct 2017, 18:45
I am confused on the solution formula used. Could someone break it down more in detail?
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Bunuel
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   24 Oct 2017, 00:18
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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.
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twash017
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   24 Oct 2017, 14:09
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!
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   12 May 2018, 05:58
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
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   12 May 2018, 10:00
If the interest is compounded anually answer D were correct.
The answer has to be very close to D though.
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   15 Nov 2019, 06:10
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


a(0.1/2)+[a+a(0.1/2)](0.1/2)=51.25
a(0.1)+[a+a(0.1)](0.1)=102.5
a+[1.1a]=1025
2.1a=1025
a=10250/21=10250/(7*3)
a~1464/3~488

Ans (C)
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Re: How much money must be invested at 10% annual interest, compounded sem [#permalink] New post   02 Oct 2023, 08:47
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