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If $1000 is placed into account X, yielding 10% interest compounded an

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If $1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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New post 01 Aug 2018, 23:21
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If $1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years?  


A. $0
B. $100
C. $110.51
D. $133.31
E. $146.41

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Re: If $1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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New post 02 Aug 2018, 01:52
S.I = P*T*R / 100 = 1000 * 5 * 0.1 = 500
C.I = P*( 1 + R/100 )^nt - P = 1000 * ( 1 + 0.1 )^5 - 1000 = 1610.51 - 1000 = 610.51

C.I - S.I = 610.51 - 500 = 110.51

Hence, C.
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Re: If $1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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New post 02 Aug 2018, 02:30
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Bunuel wrote:
If $1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years?  


A. $0
B. $100
C. $110.51
D. $133.31
E. $146.41


A simple interest of 10% every year will increase the principal by 0.1(x will become 1.1) in a year.
The principal will increase by the same time every year and becomes \(x + 5(0.1x) = 1.5x\) in 5 years.

On the contrary, the compound interest will be \(x*(1.1)^5 = x(1.331*1.21) = 1.61051x\)

The difference between the amount in account X and account Y is \(1.61051x - 1.5x = 0.11051x\)

Therefore, since the amount placed is $1000, there is 0.11051*1000 = $110.51(Option C) more in account X.
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Re: If $1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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New post 03 Oct 2018, 04:08
Bunuel wrote:
If $1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years?  


A. $0
B. $100
C. $110.51
D. $133.31
E. $146.41



Is there any way to solve this problem without calculating (1.1)5 ?
Most of the interest questions I've managed to solve it without much calculation. Wonder if this one could be solved in a different way.
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Re: If $1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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New post 03 Oct 2018, 05:19
2
Bunuel wrote:
If $1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest, how much more will be in account X than in account Y at the end of 5 years?  


A. $0
B. $100
C. $110.51
D. $133.31
E. $146.41



Approximate:

In 1st year, both interests will be the same at $100 each.
In 2nd year, CI will be $10 extra (10% interest on previous interest of $100)
In 3rd year, CI will be $21 extra (10% interest on previous interest of $100 + $110 = $210)

It's already obvious that the answer will be 110.51 (= 10 + 21 + approx (30 + a bit extra) + approx (40 + a bit extra)).

else calculate for last 2 years too.

In 4th year, CI will be $33 extra (10% interest on previous interest of $210 + $121 = $331)
In 5th year, CI will be $46 (10% interest on previous interest of $331 + $133 = $464)

Total extra = 10 + 21 + 33 + 46 = $110
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Re: If $1000 is placed into account X, yielding 10% interest compounded an &nbs [#permalink] 03 Oct 2018, 05:19
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