AJ is saving for a trip for his family and as of today has accumulated $$950$ in a trip fund. AJ's goal is to accumulate $$1900,$ or $2$ times this amount to support the trip. Assuming that all of AJ's trip fund is invested to earn an interest rate of $6\mathrm{.}00\%,$ how long, in years and in fractions of a year, will it take AJ to achieve his goal?