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An investment receives 20% annual interest compounded semi-annually fo

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New post 01 Nov 2019, 05:35
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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


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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 01 Nov 2019, 07:27
1
from given info
29200 = x * ( 1+10/100)^4
solve for x = ~ 20,000
IMO D


Bunuel 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


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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 05 Nov 2019, 13:24
Le x be the principal

x*\(1.1^4\)=29200
x=\(\frac{29200}{14641} *10000\)
=~ 20000

Hence D
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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 05 Nov 2019, 19:50
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Is there a quick way to solve for principal. I know the formula and know the cocept too but could not figure out 29200/2.2^4 = ?
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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 07 Nov 2019, 06:42
superczan wrote:
Is there a quick way to solve for principal. I know the formula and know the cocept too but could not figure out 29200/2.2^4 = ?


I think the same... I think it's very time consuming.. can somebody please give any tip to solve this fast? Thanks!
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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 19 Nov 2019, 04:12
1
the interest is compounded semi-annually so 10% every 6 months for 4 periods.

1.1x after 6 months (x+10%x)
1.21x after a year (1.10x+10%1.10x)
1.33 x after one year and six months
1.46x after two years

1.46x=29200--->x=29200/1.46=20000

hope it helps.
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Re: An investment receives 20% annual interest compounded semi-annually fo  [#permalink]

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New post 27 Nov 2019, 11:55
Bunuel 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


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We use the compound interest formula: A = P(1 + r/n)^nt, where A = the final value, P = the initial value, r = the interest rate (decimal), n = the number of compounding periods per year, and t = the number of years. We can create the equation:

29,200 = P(1 + 0.2/2)^[(2)(2)]

29,200 = P(1.1)^4

29,200 = 1.4641P

19,944 ≈ P

Answer: D
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Re: An investment receives 20% annual interest compounded semi-annually fo   [#permalink] 27 Nov 2019, 11:55
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