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Patricia invested a sum of money at an annual simple interest rate of

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Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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New post 22 Feb 2018, 19:55
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A
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Difficulty:

  45% (medium)

Question Stats:

85% (02:19) correct 15% (01:58) wrong based on 33 sessions

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Patricia invested a sum of money at an annual simple interest rate of 21/2%. At the end of 4 years the amount invested plus interest earned was $781.00. What was the dollar amount of the original investment?

(A) $231.84

(B) $318.16

(C) $550.00

(D) $750.00

(E) $781.84

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Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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New post 22 Feb 2018, 22:08
Bunuel wrote:
Patricia invested a sum of money at an annual simple interest rate of 21/2%. At the end of 4 years the amount invested plus interest earned was $781.00. What was the dollar amount of the original investment?

(A) $231.84

(B) $318.16

(C) $550.00

(D) $750.00

(E) $781.84


Formula used: Simple interest = \(\frac{P*n*R}{100}\)

Let the initial investment that Patricia made be P

\(P + \frac{P*n*R}{100} = 781\) -> \(P(1 + \frac{nR}{100}) = 781\)

Substituting n = 4, R = \(\frac{21}{2}\) in the equation, we get \(P(1 + 4*\frac{21}{2}*\frac{1}{100}) = 781 -> P(1 + \frac{42}{100}) = 781\)

Therefore, \(P * (\frac{142}{100}) = 781\) -> \(P = \frac{781*100}{142}\) = approximately $550(Option C)
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Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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New post 22 Feb 2018, 23:12
Interest rate is 11.5%

Without calculation we can derive the solution for this problem by a simple logic. The interest rate is little higher than 10% and duration is 4 years.

So the interest accumulated would be a little higher than 45-50% of the original dollar amount which is approximately 200 to 250$.

Our total amount after 4 years would be somewhere closer to 145%-150% of the original dollar amount.

781$ is the accumulated amount which is equal to 145-150% and the only logical option in our answer choice is 550$.

Ans: C
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Re: Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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New post 22 Feb 2018, 23:35
Bunuel wrote:
Patricia invested a sum of money at an annual simple interest rate of 21/2%. At the end of 4 years the amount invested plus interest earned was $781.00. What was the dollar amount of the original investment?

(A) $231.84

(B) $318.16

(C) $550.00

(D) $750.00

(E) $781.84


let principal = P

p( 1 + nr/100) = 781

p( 1+ 4x21/2 x 1/100) = 781

p( 1+42/100) = 781

p =550

(C) imo
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Re: Patricia invested a sum of money at an annual simple interest rate of &nbs [#permalink] 22 Feb 2018, 23:35
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