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

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Bunuel
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Patricia invested a sum of money at an annual simple interest rate of [#permalink] New post   22 Feb 2018, 20:55
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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] New post   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)
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Patricia invested a sum of money at an annual simple interest rate of [#permalink] New post   23 Feb 2018, 00:12
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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] New post   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
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Re: Patricia invested a sum of money at an annual simple interest rate of [#permalink] New post   28 Mar 2021, 09:50
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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

Solution:

Let P = the principal, i.e., the amount of the original investment. We can create the equation (note: 21/2% = 21/2 x 1/100 = 21/200):

P + P x 21/200 x 4 = 781

P + 21P/50 = 781

71P/50 = 781

P = 781 x 50/71 = 11 x 50 = 550

Answer: C
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Re: Patricia invested a sum of money at an annual simple interest rate of [#permalink] New post   24 May 2023, 03:38
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Re: Patricia invested a sum of money at an annual simple interest rate of [#permalink]
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