Jennifer JackPot has just won lottery. She will get $$50,000$ every $6$ months for $10$ years $(20$ payments$).$ The first payment will be coming $4\mathrm{.}5$ years from today; subsequent payments will be every $6$ months thereafter. If the discount rate is $13\mathrm{.}61\%$ compounded monthly,

a$.$ what is the present value of this annuity three years from now? and

b$.$ what is the current present value of the annuity?