Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

• Considering P as initial investment, we can say after 1 year, the value of the investment will be, after 2nd year and so on.
• From statement 1, the value of the investment at the beginning of the second year is the same as the value of the investment at the end of the first year. So, = $\$4,160.00$. We can solve this equation and determine the value of the investment for each of the 5 years.
• From statement 2, the value of the investment at the beginning of the third year is the same as the value of the investment at the end of the second year. So, = $\$4,\mathrm{326.40.}$ We can solve this equation and determine the value of the investment for each of the 5 years.