Dan wishes to purchase a new ultra high definition TV$.$ He is offered the following payment options:

Option $1$: $$0$ down

$$533\mathrm{.}20$ in $1$ year

$$400$ in $2$ years

Option $2$: $$103\mathrm{.}74$ down

$$310$ in $1$ year

$$520$ in $2$ years

Determine the range of interest rates for which the present value of Option $1$ is greater than the present value of Option $2.$