For the following amount at the given interest rate compounded continuously, find (a) the future value after 7 years, (b) the effective rate, and (c) the time to reach $\$ 11,000$.
\[
\$ 5200 \text { at } 3.3 \%
\]
a. The future value after 7 years is approximately $\$ \square$.
(Do not round until the final answer. Then round to the nearest cent as needed.)

Step 1 ：Given the present value (PV) is $5200, the interest rate (r) is 3.3% or 0.033 in decimal form, and the time (t) is 7 years.

Step 2 ：We use the formula for future value in continuous compounding: \(FV = PV * e^{rt}\), where FV is the future value, PV is the present value, r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately equal to 2.71828).

Step 3 ：Substitute the given values into the formula: \(FV = 5200 * e^{0.033*7}\)

Step 4 ：Calculate the future value: \(FV = 6551.268045136003\)

Step 5 ：Round the future value to the nearest cent to get the final answer: \(\boxed{6551.27}\)