(a) What is the correct expression for the time-0 present value of the first five payments?

(b) If, everything else remaining unchanged, the frequency of payments changes from quarterly to monthly, will the time-0 present value of the first five payments be higher, lower, or unchanged?

(c) What is the correct expression for the time-0 present value of the remaining five payments?

(d) What is the amount of the level annuity payable continuously for 10 years having the same present value as the overall cash-flows of this annuity?

(e) If, everything remaining unchanged, the level annuity payable continuously from the previous question was payable for more than 15 years instead of 10 years, will the amount of the annuity be higher, lower, or unchanged?

A cash-flow consists of an immediate annuity payable quarterly in arrears where the payments are 50 pa for the first 6 years and 80 pa for the next 4 years. Suppose that the interest rate is 8% pa convertible quarterly during the first five years, and 10% pa convertible quarterly during the remaining five years