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# If x dollars are placed in a savings account that earns y% annual inte

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
If x dollars are placed in a savings account that earns y% annual inte  [#permalink]

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07 Nov 2019, 03:19
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Difficulty:

55% (hard)

Question Stats:

57% (01:53) correct 43% (01:39) wrong based on 54 sessions

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If x dollars are placed in a savings account that earns y% annual interest compounded quarterly. What is the balance at the end of the year?

(1) If the x dollars had been in the account for 1 year longer, the amount earned in interest would have been $60 greater. (2) If 2x dollars had been in the account for 18 months, the interest would have been$75 greater.

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Joined: 19 Oct 2018
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Re: If x dollars are placed in a savings account that earns y% annual inte  [#permalink]

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02 Dec 2019, 11:47
1
Let P is the balance at the end of the year

$$P= x(1+\frac{y}{400})^4$$

We need to figure out both x and y in order to figure out balance at the end of the year.

Statement 1-

$$x(1+\frac{y}{400})^8- x(1+\frac{y}{400})^4= 60$$

we have 2 variables and 1 equation

Insufficient

Statement 2-

$$2x(1+\frac{y}{400})^{18/4}- x(1+\frac{y}{400})^4= 75$$

we have 2 variables and 1 equation

Insufficient

Combining 2 statements, we have 2 variables and 2 equations; hence, we can figure out x and y.

Sufficient

Bunuel wrote:
If x dollars are placed in a savings account that earns y% annual interest compounded quarterly. What is the balance at the end of the year?

(1) If the x dollars had been in the account for 1 year longer, the amount earned in interest would have been $60 greater. (2) If 2x dollars had been in the account for 18 months, the interest would have been$75 greater.

Are You Up For the Challenge: 700 Level Questions
Re: If x dollars are placed in a savings account that earns y% annual inte   [#permalink] 02 Dec 2019, 11:47
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# If x dollars are placed in a savings account that earns y% annual inte

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