Nasha is searching for the best way to invest her $$40,000.$ One financial institution offers $4\%$ on threemonth term deposits and $4\mathrm{.}5\%$ on six$-$month term deposits. Nasha is considering either doing two back$-$to$-$back three$-$month term deposits $($option $1)$ or just taking the six$-$month deposit $($option $2).$ It is almost certain that interest rates will rise by $0\mathrm{.}5\%$ before her first three$-$month term is up$.$ With option $1,$ she would place the simple interest and principal from the first three$-$month term deposit into the second three$-$month deposit.

Calculate the interest earned under each option. Round your answers to two decimal places.

Interest earned under option $1$:

Interest earned under option $2$: $

How much more interest does Nasha make under the best option?

Additional interest earned: $