Which of the following annuities has the lowest present value? Where applicable, use the same compounding pattern for the deferred years as for the years payments were made.

Select one:

a$.$ A series of $8$ annual payments of $$4,000$ paid on the first day of the year for each of the next $8$ years $($compounded annually$)$ with an interest rate of $9\%.$

b$.$ A series of payments of $$2,250$ paid on the last day of each six$-$month period $($compounded semiannually$)$ for $7$ years with an interest rate of $9\%.$

c$.$ No payments made for two years and then the same payment pattern as A$.$

d$.$ No payments made for one year and then the same payment pattern as B$.$

e$.$ Both A and C are equal and the lowest.

f$.$ Both B and D are equal and the lowest.