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John has been saving $x annually since 3 years ago, and the interest r

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John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  13 May 2017, 18:50
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John has been saving $x annually since 3 years ago, and the interest rate for his savings increased r% annually. After saving the money for 3 years as such, he withdrew all the money in the account and spent it all in one year. If he spent a constant amount per each month, how much money did he spend each month in terms of x and r?

(A) x/2 (1+r/100)

(B) x/4 (1+r/100)

(C) x/6 (1+r/100)

(D) x/4 (1+r/50)

(E) x/4 (1+r/25)

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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  23 May 2017, 12:40
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It took me 5+ minute to solve the question - at the end I had to put the values r=10% and calculate the value of the amount with approximation the result was close to option D; I marked it and went ahead. Not much pathetic approach would exist than this one.
Please help me by posting the method to solve the question.
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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  24 May 2017, 05:59
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hazelnut wrote:
John has been saving $x annually since 3 years ago, and the interest rate for his savings increased r% annually. After saving the money for 3 years as such, he withdrew all the money in the account and spent it all in one year. If he spent a constant amount per each month, how much money did he spend each month in terms of x and r?

(A) x/2 (1+r/100)

(B) x/4 (1+r/100)

(C) x/6 (1+r/100)

(D) x/4 (1+r/50)

(E) x/4 (1+r/25)


Bad question, because the answer assumed simple interest rate, however, the text of the question assumed compound interest rate.
How I've solved this question:
1st-year money: x*(1+r/100), 2nd year: x*(1+2r/100), 3rd: x(1+3r/100).
Add this together and divide by 12 (months): (3x+6r/100)/12=x/4*(1+r/50).

However, my initial assumption was: (x*(1+r/100)*(1+2r/100)*(1+3r/100))/12, but this definitely would not result in any answer given.
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Shreshtha55
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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  25 Jun 2019, 13:30
chetan2u can you please explain the answer to me! I am a bit confused with what the question is asking.
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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  25 Jun 2019, 20:34
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Hi,
The question is of a very poor quality. What does interest rate INCREASES r% annually mean and various other faults. Just leave it.
Otherwise, in such questions assume X as 1000 and r as 10 and check choices with your answer.

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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  26 Jun 2019, 11:04
the question should indicate if it is simple interest or compound interest. if it is compound then b is d ans.

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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  15 Apr 2020, 09:26
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hazelnut wrote:
John has been saving $x annually since 3 years ago, and the interest rate for his savings increased r% annually. After saving the money for 3 years as such, he withdrew all the money in the account and spent it all in one year. If he spent a constant amount per each month, how much money did he spend each month in terms of x and r?

(A) x/2 (1+r/100)

(B) x/4 (1+r/100)

(C) x/6 (1+r/100)

(D) x/4 (1+r/50)

(E) x/4 (1+r/25)


The problem is worded poorly. Let’s assume the annual interest rate is a constant r%.

The $x he saved 3 years ago is now x(1 + 3r/100).

The $x he saved 2 years ago is now x(1 + 2r/100).

The $x he saved 1 year ago is now x(1 + r/100).

Therefore, the total he can withdraw now is x(3 + 6r/100) = 3x(1 + 2r/100) = 3x(1 + r/50). Since he withdraws this amount in 12 equal payments, he receives 3x(1 + r/50)/12 = x(1 + r/50)/4 in each payment.

Answer: D
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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink] New post  09 Feb 2022, 15:46
First of all I cannot comprehend this "the interest rate for his savings increased r% annually"

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Re: John has been saving $x annually since 3 years ago, and the interest r [#permalink]
09 Feb 2022, 15:46
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