enigma123 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