How long will it take for $5700 to grow two 34,800 and interest-rate of 3.8% but the interest is compounded continuously

For continuous compounding, the formula is:

A = Pe

^{rt}Where A = Final amount of money, P = initial investment (principle), r = annual interest rate (expressed as a decimal value), t= time in years. To solve for t:

ln(A) = ln(Pe

^{rt}) = ln(P) + ln(e^{rt}) = ln(P) + rtln(A) - ln(P) = rt

ln(A/P)/r = t

Plug in the values (remember r = 0.038) and solve for t.