QuestionUse the savings plan formula to answer the following question.
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of $6 \%$. How much should you deposit monthly to accumulate $\$ 86,000$ in 17 years?
You should invest \$$\square$ each month. (Do not round until the final answer. Then round to two decimal places as needed.)

Studdy Solution
Solve for the monthly deposit $P$.
First, calculate the term inside the parentheses:
$ 1 + \frac{0.06}{12} = 1 + 0.005 = 1.005 \]
Next, calculate the exponent:
$ 12 \times 17 = 204 \]
Now, calculate the power:
$ (1.005)^{204} \]
Calculate the entire fraction:
$ \frac{(1.005)^{204} - 1}{0.005} \]
Finally, solve for $P$:
$ P = \frac{86,000}{\frac{(1.005)^{204} - 1}{0.005}} \]
Calculate the value of $P$ using a calculator:
$ P \approx 208.67 \]
Therefore, you should invest approximately $\boxed{208.67}$ each month.