Calculate the following present value for the following annuities.

a. Dan will be collecting his retirement benefit starting one month from now and continuing for 25 years. He will receive 3000 per month for the first year and the monthly benefit increases by 3% per year. At the rate of 5% annual interest compounded monthly, calculate the present value of the retirement benefit.

b. A 10-year decreasing annuity-immediate, with annual payments of 20, 18, 16, , 2. Given an effective rate of 6%.

c. A perpetuity-immediate with annual payments. The perpetuity pays 1 in year 1, 2 in year 2, 3 in year 3, and so on, until year 10 where it pays 10 every year from then on. Given an effective rate of 6%.