Multiple choice

A certain investment earned a fixed rate of 4 percent interest per year, compounded annually, for five years. The interest earned for the third year of the investment was how many dollars greater than that for the first year? 1. The amount of the investment at the beginning of the second year was \$4,160.00. 2. The amount of the investment at the beginning of the third year was \$4,326.40.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest for year n is P(1+r)^(n-1) * r. With r=0.04, interest in year 3 is P(1.04)^2 * 0.04 and year 1 is P * 0.04. The difference is P * 0.04 * ((1.04)^2 - 1). Both statements provide the principal at the start of a year, which allows calculating P.

AI explanation

Let the principal be P. The amount at the beginning of the second year is 1.04P, so statement (1) gives 1.04P = 4160, which yields P = 4000. The first year interest is 4% of 4000, which is 160. The third year amount is 4000(1.04)^3 = 4499.46, making the third year interest equal to 4% of the second year amount (4160), which is 166.40. The difference is 166.40 - 160 = 6.40. Using statement (2), the amount at the beginning of the third year is 4326.40, so the second year amount is 4326.40 / 1.04 = 4160. The first year amount is 4160 / 1.04 = 4000, which provides the exact same principal and difference. Therefore, each statement alone is sufficient to find the difference.

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