Level and Increasing annuities

Question 1

Define I a n
and write out proof

Answer 1

Present value of payments 1 at the end of the first period, 2 at the end of the second period,…and n at the end of the nth time period

multiply by (1+i) on both sides

Question 2

Define and prove Ia:n

Answer 2

present value of an increasing annuity due payble for n time units, the tth payment (of amount t) is made at t-1

multiply by v on both sides

Question 3

Define(in words and algebraically) and prove I [a]n

Answer 3

increasing annuity which is payable continously by constant rate of payment of r per unit time throughout the rth period

Question 4

Define (in words and algebraically) and prove [Ia]n

Answer 4

increasing annuity payble continously payable by rate of t at time t

Question 5

Define(in words and algebraically) and prove [a]n

Answer 5

present value of an annuity payble continously between 0 and n, where the rate of payment per unit time is constant and equal to 1