(a) You just turned 30. You want to buy an annuity which will pay 1000 per year on each of your 65th through 80th birthdays. How much is that annuity worth today? (

b) You buy an annuity which pays 100 at times 0, 1, 2, · · ·, 29. You need to pay for it at time 15. How much will it cost?

(c) You buy an annuity which pays 100 at times 0, 1, 2, · · ·, 29. You need to pay for it when you turn to 45. How much will it cost?