Consider modifying the pricing formulas for perpetuities and annuities to allow for different payment frequencies. Suppose each annual payment C is paid in n installments, spread equally over each year, and let r denote the nominal annual interest rate. For annuities, do not confuse the payment frequency n with the term T.

(a) (10) Show that the present value of a perpetuity does not depend on the payment frequency. (b) (10) Show that the present value of an annuity is increasing in the number of payments per year.

(b) What if the payments are made continuously throughout the year?