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02 Aug 2018, 00:21
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:35) correct
32%
(02:08)
wrong
based on 201
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History
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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
A. $0
B. $100
C. $110.51
D. $133.31
E. $146.41
02 Aug 2018, 02:52
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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.
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.
02 Aug 2018, 03:30
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Bunuel
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.
