QuestionRafael plans to set aside money for his young daughter's college tuition. He will deposit money in an ordinary annuity that earns $3.6 \%$ interest, compounded quarterly. Deposits will be made at the end of each quarter.
How much money does he need to deposit into the annuity each quarter for the annuity to have a total value of $\$ 72,000$ after 15 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. \$$\square$

Studdy Solution
Solve for the unknown variable $P$.
First, calculate $(1 + 0.009)^{60}$:
$$(1 + 0.009)^{60} = 1.009^{60}$$
Calculate this value using a calculator:
$$1.009^{60} \approx 1.718186$$
Now substitute back into the equation:
$$72,000 = P \times \frac{1.718186 - 1}{0.009}$$
$$72,000 = P \times \frac{0.718186}{0.009}$$
$$72,000 = P \times 79.798444$$
Finally, solve for $P$:
$$P = \frac{72,000}{79.798444}$$
$$P \approx 902.23$$
Rafael needs to deposit approximately $\boxed{902.23}$ dollars each quarter.