Use the formula for the sum of a geometric sequence to solve the problem. After a sales clerk works six months, her employer will begin an annuity for her and will contribute $550 every six months to a fund that pays 6% annual interest. After she has been employed for three years, what will be the amount of the annuity? Round your answer to the nearest cent.
A) $3,554.62
B) $3,565.25
C) $3,557.63
D) $3,487.63

Question

Quizplus · Accepted Answer

The monthly interest rate is calculated as:
i = (1 + 0.06)^(1/2) - 1
i = 0.02949

The number of periods is:
n = 6 x 2 = 12

The amount of the annuity is calculated as:
S = a[(1 + i)^n - 1] / i
S = 550[(1 + 0.02949)^12 - 1] / 0.02949
S = 3,557.63

Therefore, the amount of the annuity after three years will be $3,557.63. The answer is choice C.

Use the Formula for the Sum of a Geometric Sequence