An investment receives 20% annual interest compounded semi-a : GMAT Problem Solving (PS)
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# An investment receives 20% annual interest compounded semi-a

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17 Dec 2012, 17:41
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An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment? A.$ 17,000
B. $18,000 C.$ 19,000
D. $20,000 E.$ 21,000

A fast method to solve it?
Thanks!
[Reveal] Spoiler: OA
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17 Dec 2012, 19:30
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danzig wrote:
An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment? A.$ 17,000
B. $18,000 C.$ 19,000
D. $20,000 E.$ 21,000

A fast method to solve it?
Thanks!

Formula to calculate compound interest:
$$A=P[1 + R/100]^t$$
Where P= initial amount
R= annual rate
t=time given

Whenever we are supposed to calculate the quarterly CI or semi-annually CI, remember one thing:
For quarterly calculations: Divide the rate by 4 and multiply the time by 4
For semi-annually calculations: Divide the rate by 2 and multiply the time by 2.

On applying the mentioned concept:
$$29200=P * (1.1)^4$$

$$(1.1)^4 is 1.4$$ approximately. In order to make the calculations simpler, because the question is asking "approximately", we can assume this 1.4 as 1.46. This is because 1.46*2=2.92.

Now on solving, we get P as 20000.
Hope that helps.
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18 Dec 2012, 07:43
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Marcab wrote:
danzig wrote:
An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment? A.$ 17,000
B. $18,000 C.$ 19,000
D. $20,000 E.$ 21,000

A fast method to solve it?
Thanks!

Formula to calculate compound interest:
$$A=P[1 + R/100]^t$$
Where P= initial amount
R= annual rate
t=time given

Whenever we are supposed to calculate the quarterly CI or semi-annually CI, remember one thing:
For quarterly calculations: Divide the rate by 4 and multiply the time by 4
For semi-annually calculations: Divide the rate by 2 and multiply the time by 2.

On applying the mentioned concept:
$$29200=P * (1.1)^4$$

$$(1.1)^4 is 1.4$$ approximately. In order to make the calculations simpler, because the question is asking "approximately", we can assume this 1.4 as 1.46. This is because 1.46*2=2.92.

Now on solving, we get P as 20000.
Hope that helps.

You are explanation Marcab is really good (indeed it is).

At the same time the key concept to keep in mind is that interest compound annually, semestral and so on are simply % increase or decrease, one after another.

Similarly, we have 100 and we have a discount of 20% and then 10 % . We have , of course, 80 and after this 10% of 80.

Here is the same.

here we have 20% 2 times per year so: 10% or 1.1 for two years. $$1.1^4$$or 1.1 four times.

if we have the original amount X and the finel amount 29,200. We need only to divide$$\frac{29,200}{1.1}$$ the result again 1.1 for four times.the result is $$19943$$. We have approximately.

Thinking about compound interest as successive % is pretty straight. That's it
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18 Dec 2012, 17:44
Could you explain with more detail this part, please? How did you find that $$1.1^4 = 1.4$$ without making the calculations? Also, I don't understand why you mentioned this: 1.46*2 = 2.92. Thanks!

Marcab wrote:
$$(1.1)^4 is 1.4$$ approximately. In order to make the calculations simpler, because the question is asking "approximately", we can assume this 1.4 as 1.46. This is because 1.46*2=2.92.
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18 Dec 2012, 17:54
danzig wrote:
Could you explain with more detail this part, please? How did you find that $$1.1^4 = 1.4$$ without making the calculations? Also, I don't understand why you mentioned this: 1.46*2 = 2.92. Thanks!

Marcab wrote:
$$(1.1)^4 is 1.4$$ approximately. In order to make the calculations simpler, because the question is asking "approximately", we can assume this 1.4 as 1.46. This is because 1.46*2=2.92.

Please danzing refer to my previous post. Is all explained well and totally.

Thanks
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18 Dec 2012, 19:12
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Hii danzig.
See there is a pattern:
1.1^1=1.1,
1.1^2~1.2,
1.1^3~1.3,
1.4^4~1.4
since the question is asking "approximately" therefore I change 1.4 to 1.46.
Why only 1.46?
Because 1.46 *2=2.92. Since the final is given in terms of 292 only, therefore It simplifies the calculation
Hope that helps.
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11 Jul 2016, 10:19
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Re: An investment receives 20% annual interest compounded semi-a   [#permalink] 11 Jul 2016, 10:19
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