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14 Oct 2023, 12:04
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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:
67% (01:36) correct
33%
(02:01)
wrong
based on 720
sessions
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If a sum of money, \(P\) dollars, is invested at the interest rate of \(i\)% per year, compounded annually, and \(n\) is a positive integer, the value of the investment after \(3n\) years will be how many times as great as the value of the investment after \(2n\) years?
A. \((1+\frac{i}{100})\)
B. \((1+\frac{i}{100})^{3/2}\)
C. \((1+\frac{i}{100})^n\)
D. \(p(1+\frac{i}{100})^{3/2}\)
E. \(p(1+\frac{i}{100})^n\)
A. \((1+\frac{i}{100})\)
B. \((1+\frac{i}{100})^{3/2}\)
C. \((1+\frac{i}{100})^n\)
D. \(p(1+\frac{i}{100})^{3/2}\)
E. \(p(1+\frac{i}{100})^n\)
14 Oct 2023, 13:16
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yrozenblum
If a sum of money, \(P\) dollars, is invested at the interest rate of \(i\)% per year, compounded annually, and \(n\) is a positive integer, the value of the investment after \(3n\) years will be how many times as great as the value of the investment after \(2n\) years?
A. \((1+\frac{i}{100})\)
B. \((1+\frac{i}{100})^{3/2}\)
C. \((1+\frac{i}{100})^n\)
D. \(p(1+\frac{i}{100})^{3/2}\)
E. \(p(1+\frac{i}{100})^n\)
A. \((1+\frac{i}{100})\)
B. \((1+\frac{i}{100})^{3/2}\)
C. \((1+\frac{i}{100})^n\)
D. \(p(1+\frac{i}{100})^{3/2}\)
E. \(p(1+\frac{i}{100})^n\)
Value of the investment after 3n years = \(P(1+\frac{i}{100})^{3n}\)
Value of the investment after 2n years = \(P(1+\frac{i}{100})^{2n}\)
Let's assume that the value of the investment after \(3n\) years is \(k\) times greater than the value of the investment after \(2n\) years. We have to find the value of \(k\)
\(P(1+\frac{i}{100})^{3n} = k*P(1+\frac{i}{100})^{2n}\)
Dividing both sides by \(P(1+\frac{i}{100})^{2n}\)
\(k = (1+\frac{i}{100})^{3n-2n}\)
\(k = (1+\frac{i}{100})^{n}\)
Option C
General Discussion
16 Oct 2023, 21:27
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From Relative Change formula : % increase = Increase ÷ Original Number × 100.
[ \(P(1+\frac{i}{100})^{3n}\) - \(P(1+\frac{i}{100})^{2n}\) ] / \(P(1+\frac{i}{100})^{2n}\) (without x 100 to find the value represent in number instead of percentage)
[ \(P(1+\frac{i}{100})^{3}\) / \(P(1+\frac{i}{100})^{2}\) ] - 1
\(P(1+\frac{i}{100})^{3/2}\) - 1
\(P(1+\frac{i}{100})^{3/2}\) - 1 + 1 to find how much times it greater/lower than the original value
\(P(1+\frac{i}{100})^{3/2}\)
but why I can't find the similarity to the correct answer C instead I got answer B?
[ \(P(1+\frac{i}{100})^{3n}\) - \(P(1+\frac{i}{100})^{2n}\) ] / \(P(1+\frac{i}{100})^{2n}\) (without x 100 to find the value represent in number instead of percentage)
[ \(P(1+\frac{i}{100})^{3}\) / \(P(1+\frac{i}{100})^{2}\) ] - 1
\(P(1+\frac{i}{100})^{3/2}\) - 1
\(P(1+\frac{i}{100})^{3/2}\) - 1 + 1 to find how much times it greater/lower than the original value
\(P(1+\frac{i}{100})^{3/2}\)
but why I can't find the similarity to the correct answer C instead I got answer B?
