Solve the problem. Round to the nearest cent.
-Cara needs $9,000 in 12 years. What amount can she deposit at the end of each quarter at 6% interest compounded quarterly so she will have her $9,000?
A) $125.68
B) $133.23
C) $533.49
D) $129.37

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of an annuity: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value ($9,000), $P$ is the payment per period (what we're solving for), $r$ is the interest rate per period (6% annually or 0.06, divided by 4 quarters gives 0.015 per quarter), and $n$ is the total number of payments (12 years times 4 quarters/year gives 48 quarters). Rearranging the formula to solve for $P$ gives $P = FV / \left( \frac{(1 + r)^n - 1}{r} \right)$. Plugging in the values gives $P = 9000 / \left( \frac{(1 + 0.015)^{48} - 1}{0.015} \right)$, which calculates to approximately $129.37 when rounded to the nearest cent.

Solve the Problem. Round to the Nearest Cent