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If a sum of money, P dollars, is invested at the interest rate of i% p

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yrozenblum
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If a sum of money, P dollars, is invested at the interest rate of i% p [#permalink] New post   14 Oct 2023, 12:04
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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. \(p(1+\frac{i}{100})^n\)
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C
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gmatophobia
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Re: If a sum of money, P dollars, is invested at the interest rate of i% p [#permalink] New post   14 Oct 2023, 13:16
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yrozenblum wrote:
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. \(p(1+\frac{i}{100})^n\)


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
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sanebeyondone
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If a sum of money, P dollars, is invested at the interest rate of i% p [#permalink] New post   16 Oct 2023, 21:27
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?
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ruis
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Re: If a sum of money, P dollars, is invested at the interest rate of i% p [#permalink] New post   03 Mar 2024, 11:19
sanebeyondone wrote:
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?

I think you do not need to substract 1.
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Re: If a sum of money, P dollars, is invested at the interest rate of i% p [#permalink]
03 Mar 2024, 11:19
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