Melisandre has a geometric annuity immediate. Payments are made at the start of each six months for 3 years, and the initial payment is $150.00. The growth rate for the payments is r = 1.350% and the effective intererst rate per period is i = 1.375%.

a) What is the future value of her annuity?

b) If the growth rate changes to exactly match the effective interest rate per period (i = r), what is the future value of her payments?