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On May 1 of last year, Jasmin invested x dollars . . . .

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On May 1 of last year, Jasmin invested x dollars . . . .

by Vincen » Mon Jan 29, 2018 3:12 am
On May 1 of last year, Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

(1) As of June1 of last year, the investment had earned $200 in interest.
(2) As of July 1 of last year, the investment had earned $401 in interest.

The OA is the option D.

I need some help here? Experts can you help me? I don't know how to solve this DS question. <i class="em em-disappointed"></i>
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by alanforde800Maximus » Fri May 18, 2018 1:13 am
Bumping for experts review.
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by GMATGuruNY » Fri May 18, 2018 2:15 am
Vincen wrote:On May 1 of last year, Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

(1) As of June1 of last year, the investment had earned $200 in interest.
(2) As of July 1 of last year, the investment had earned $401 in interest.
Statement 1:
Since we know the interest rate (6% per year, compounded monthly) and the amount of interest earned after one month ($200), we can calculate the amount Jasmin must have invested.
SUFFICIENT.

Statement 2:
Since we know the interest rate (6% per year, compounded monthly) and the amount of earned earned after two months ($401), we can calculate the amount Jasmin must have invested.
SUFFICIENT.

The correct answer is D.

Since the 6% annual interest is compounded monthly over a 12-month period, the percentage earned each month = (6/12)% = 0.5% = (0.5)/100 = 5/1000 = 1/200.
Statement 1 indicates that $x earns $200 of interest in the first month:
(1/200)x = 200
x = 40,000.
Resulting amount in the account = 40,000 + 200 = 40,200.
Since the account holds $40,200 in the second month, the interest earned in the second month is as follows:
(1/200)(40,200) = 201.
Total interest earned over two months = (first-month interest) + (second-month interest) = 200 + 201 = 401.
The value in blue is the information given in Statement 2.
This value will be yielded only if x = 40,000 (the value required by Statement 1).
Thus, each statement implies that x = 40,000.
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by Jeff@TargetTestPrep » Mon May 21, 2018 3:58 pm
Vincen wrote:On May 1 of last year, Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value of x?

(1) As of June1 of last year, the investment had earned $200 in interest.
(2) As of July 1 of last year, the investment had earned $401 in interest.
We are given that Jasmin invested x dollars in a new account at an interest rate of 6 percent per year, compounded monthly, on May 1 of last year. In that case, the total amount A (principal plus interest) after m months will be A = x(1 + 0.06/12)^m or A = x(1.005)^m. Since the principal is x, then the total interest earned during the same period is A - x = x(1.005)^m - x = x(1.005^m - 1).

Statement One Alone:

As of June 1 of last year, the investment had earned $200 in interest.

We see that m = 1 since only 1 month passed from May 1 to June 1, so we can create the equation x(1.005^1 - 1) = 200. Without actually solving for x, we see that the equation is solvable for x. So statement one is sufficient.

Statement Two Alone:

As of July 1 of last year, the investment had earned $401 in interest.

We see that m = 2 since 2 months passed from May 1 to July 1, so we can create the equation x(1.005^2 - 1) = 401. Without actually solving for x, we see that the equation is solvable for x. So statement two is also sufficient.

Answer: D

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