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17 Jan 2017, 10:04
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:07) correct
39%
(02:13)
wrong
based on 397
sessions
History
Date
Time
Result
Not Attempted Yet
How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?
A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00
A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00
24 Oct 2017, 00:17
Kudos
Bookmarks
twash017
How much money must be invested at 10% annual interest, compounded semi-annually, in order to earn $51.25 in interest income by the end of the year?
A. $1,025.00
B. $512.50
C. $500.00
D. $256.25
E. $42.00
10% annual interest, compounded semi-annually means that the investment earns 5% in every 6 months.
So, we are looking for such x, which satisfies: x*1.05^2 = x + 51.25
0.1025x = 51.25;
1025x = 512500;
x = 500.
Answer: C.
Another way: since 10% annual interest is compounded semi-annually, then the actual interest will be a little bit more that 10% (because of the interest earned on interest). Thus, $51.25 of interest must be a little bit more that 10% of the correct answer. Only C fits.
Answer: C.
General Discussion
17 Jan 2017, 10:45
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Bunuel
Algebraic approach
CI=P*(1+r/100)^t
CI=P+51.25
thus P+51.25=P(1+10/(2*100)^2
P=500
2nd logical approach
10% of 500 =50
thus total profit is a bit more since interest earned compounded basis
thus profit must be 51.25
(check for first year 500+25=525
second year 525*5/100=26.25
total 525+26.25= 551.25)
Thus Ans C
