AccordingtotheInternationalInstituteofSocialHistory $($Amsterdam$),$ the amount of money used to purchase Man hattan Island in $1626$ is valued at $$1,050$ in terms of today$$s dollars. If that amount were instead invested in an account that pays $4\%$ per annumwithcontinuous compounding, what would be the value of the investment in $2020?$ Compare with the case that interest is paid at $6\%$ per annum.