Mary deposited sum of x dollars into an account that earned 4% annual

Question

Mary deposited sum of x dollars into an account that earned 4% annual interest compounded annually. One year later she deposited additional x dollars in the account. Consider that there were no other transactions and if the account showed y dollars at the end of the two years, which of the following expresses x in terms of y?

(A) \(\frac{y}{2.04}\)

(B) \(\frac{y}{1.12}\)

(C) \(\frac{y}{2.2}\)

(D) \(\frac{y}{1.04 × 2.04}\)

(E) \(\frac{y}{(1.04)^2 × 2.04}\)

Show Answer

Official Answer

D

(A)  \frac{y}{2.04}

(B)  \frac{y}{1.12}

(C)  \frac{y}{2.2}

(D)  \frac{y}{1.04 × 2.04}

(E)  \frac{y}{(1.04)^2 × 2.04}

MBAHOUSE · Answer

This question is almost the same question #155 in the official guide 2022.

r2raaz · Answer

Here, after 2nd year x dollar become= x* (1+4/100)^2= x * 1.04^2
after 1st year, x dollar deposited will accumulate= x * (1+4/100)=x+1.04
Given that, x * 1.04^2 +x * 1.04= Y
 =>x* (1.04^2+1.04)=Y 
 =>x= Y/(1.04^2+1.04) (ANS)

GmatPoint · Answer

Amount after 1 year = x*(1+4/100)
After the addition of x dollars, amount = x*(2+4/100)

After 1 more year,
Amount = x*(2+4/100)*(1+4/100) = x*(51/25)(26/25)

Thus, y = x*(51/25)*(26/25)
x = y*(25/51)*(25/26)
= y/(2.04)*(1.04)

Thus, the correct option is D.

bumpbot · Answer

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Mary deposited sum of x dollars into an account that earned 4% annual

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