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

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Math Expert
Joined: 02 Sep 2009
Posts: 59561
Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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22 Feb 2018, 20:55
00:00

Difficulty:

35% (medium)

Question Stats:

81% (02:20) correct 19% (02:20) wrong based on 44 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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Joined: 26 Feb 2016
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Patricia invested a sum of money at an annual simple interest rate of  [#permalink]

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22 Feb 2018, 23:08
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 $550(Option C) _________________ You've got what it takes, but it will take everything you've got Senior Manager Joined: 31 May 2017 Posts: 334 Patricia invested a sum of money at an annual simple interest rate of [#permalink] ### Show Tags 23 Feb 2018, 00:12 Interest rate is 11.5% Without calculation we can derive the solution for this problem by a simple logic. The interest rate is little higher than 10% and duration is 4 years. So the interest accumulated would be a little higher than 45-50% of the original dollar amount which is approximately 200 to 250$.

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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23 Feb 2018, 00:35
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
Re: Patricia invested a sum of money at an annual simple interest rate of   [#permalink] 23 Feb 2018, 00:35
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