How much money must be deposited today to become ​$1300 in 20 years at 7.5% compounded​ continuously?

Use the formula for Amount for continuous compounding:

A = Pe^(rt)

Here A = $1300, r = 0.075 and t = 20 yrs.  Thus,

1300 = P*e^(0.075*20), or    1300 = P (4.482).
                                   $1300
Solving for P:  P = ----------------- = $290.07  (answer)
                                   4.482