A trust will provide $12,000 to a county library at the beginning of each 3-month period for the next 5.5 years. If the money is worth an annual rate of 7%, compounded quarterly, find the amount in the trust when it begins. Round your answer to the nearest cent.
A) $429,003.79
B) $221,370.59
C) $475,687.16
D) $546,131.86
E) $173,679.98

Question

A trust will provide $12,000 to a county library at the beginning of each 3-month period for the next 5.5 years. If the money is worth an annual rate of 7%, compounded quarterly, find the amount in the trust when it begins. Round your answer to the nearest cent. ​
A) $429,003.79
B) $221,370.59
C) $475,687.16
D) $546,131.86
E) $173,679.98

Quizplus · Accepted Answer

The amount in the trust can be calculated using the formula for the present value of an annuity: $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $PV$ is the present value (initial amount in the trust), $P$ is the payment amount ($12,000), $r$ is the interest rate per period (7% annually compounded quarterly is 0.07/4 = 0.0175 per quarter), and $n$ is the total number of payments (5.5 years = 22 quarters). Plugging in the values: $PV = 12000 \times \left[\frac{1 - (1 + 0.0175)^{-22}}{0.0175}\right]$, which calculates to approximately $221,370.59.

A Trust Will Provide $12,000 to a County Library at the Beginning