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07 May 2021, 06:15
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D
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:
66% (02:26) correct
34%
(02:46)
wrong
based on 150
sessions
History
Date
Time
Result
Not Attempted Yet
Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?
A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined
A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined
08 May 2021, 09:15
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Bunuel
Let the amounts deposited on both accounts be $100.
Then we'd have that \(100 + 100*0.22 + 100*0.22=100(1+r)^2\);
\(144=100(1+r)^2\);
\((1+r)^2=1.44\);
\(1+r=1.2\);
\(r=0.2\).
Answer: D.
General Discussion
07 May 2021, 12:23
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Let's first talk about the first account (Simple interest saving account).
Interest in the first year = 22%;
Interest in the second year = 22%; Interest does not compound in case of simple interest.
Total interest in two years = 2*22% = 44%
Now, let's talk about the second account (Compound interest saving account).
Interest in the first year = r%;
Interest in the second year = r% + (r% of r%); Interest gets compounded in case of compound interest.
Total interest in two years = r% + (r% + r% of r%) = 2r% + r%*r% = r%(2 + r%)
We know that after two years, the interests are same from both the accounts, thus,
44% = r%(2 + r%)
44 = r(2 + r/100)
Solving for r would involve handling a quadratic equation, which may be time-consuming. Let's think of another approach.
Let's plug-in the values from the options. Since option D = 20 is the easiest one to handle, let's try this first.
@r = 20, the value of r(2 + r/100) = 20(2 + 20/100) = [20*2 + (20*20/100)] = 40 + 4 = 44%. It matches the desired result. Thus, option D is the correct answer.
The correct answer: D
Interest in the first year = 22%;
Interest in the second year = 22%; Interest does not compound in case of simple interest.
Total interest in two years = 2*22% = 44%
Now, let's talk about the second account (Compound interest saving account).
Interest in the first year = r%;
Interest in the second year = r% + (r% of r%); Interest gets compounded in case of compound interest.
Total interest in two years = r% + (r% + r% of r%) = 2r% + r%*r% = r%(2 + r%)
We know that after two years, the interests are same from both the accounts, thus,
44% = r%(2 + r%)
44 = r(2 + r/100)
Solving for r would involve handling a quadratic equation, which may be time-consuming. Let's think of another approach.
Let's plug-in the values from the options. Since option D = 20 is the easiest one to handle, let's try this first.
@r = 20, the value of r(2 + r/100) = 20(2 + 20/100) = [20*2 + (20*20/100)] = 40 + 4 = 44%. It matches the desired result. Thus, option D is the correct answer.
The correct answer: D
