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: \(\boxed{6551.27}\)