Final answer:
The value of the account after 10 months with a 3.6% interest rate compounded monthly is approximately $7825.21, which matches option (c) in the student's choices.
Step-by-step explanation:
The student's question involves calculating the future value of an investment with compound interest. To solve this problem, the formula for compound interest is used:
FV = P \(\left(1 + \frac{r}{n}\right)^{nt}\)
In the given problem, P = $7500, r = 0.036 (3.6%), n = 12 (monthly compounding), and t = 10/12 years (10 months). Plugging these values into the formula:
FV = 7500 \(\left(1 + \frac{0.036}{12}\right)^{12\times\frac{10}{12}}\)
After calculating the above expression, the future value (FV) after 10 months would be approximately $7825.21, which matches option (c) $7825.21.