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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 _________________ Retired Moderator D Joined: 30 Jan 2015 Posts: 788 Location: India Concentration: Operations, Marketing GPA: 3.5 Re: If$1000 is placed into account X, yielding 10% interest compounded an  [#permalink]

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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] ### Show Tags 1 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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Joined: 22 May 2018
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Re: If $1000 is placed into account X, yielding 10% interest compounded an [#permalink] ### Show Tags 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.
Thanks!
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Joined: 16 Oct 2010
Posts: 10119
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Re: If $1000 is placed into account X, yielding 10% interest compounded an [#permalink] ### Show Tags 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 [#permalink] ### Show Tags VeritasKarishma wrote: 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

I don't fully understand how you get to YR3 interest. I thought the interest payments would be as follows

1st: 100
2nd: 100+10
3rd: 100+10+1
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If $1000 is placed into account X, yielding 10% interest compounded an [#permalink] ### Show Tags 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

Given: $1000 is placed into account X, yielding 10% interest compounded annually and$1000 is placed into account Y using 10% simple annual interest,

Asked: How much more will be in account X than in account Y at the end of 5 years?

For simple interest account Y
Interest for 5 years = 1000 * 5 * 10% = $500 Balance in simple interest account Y after 5 years =$1500

For compound interest account X
Balance in compound interest account after 5 years = 1000 (1.1)^5 where 1.1^5 = 1.61051
Balance in compound interest account X after 5 years = 1000 (1.1)^5 = $1610.51 How much more will be in account X than in account Y at the end of 5 years =$1610.51 - $1500 =$110.51

IMO C If $1000 is placed into account X, yielding 10% interest compounded an [#permalink] 17 Aug 2019, 08:56 Display posts from previous: Sort by # If$1000 is placed into account X, yielding 10% interest compounded an  