a) Define an arithmetic annuity immediate with n payments. b) Give the formula for the present value of an arithmetic annuity immediate with n payments starting at $1 and increasing by $1 each period if the effective interest rate per period is r. Satoshi is saving for retirement. At the end of the first year he deposits $8000. Each year after that he deposits $450 more than the year before. The interest rate is 4% compounded semi-annually. c) How much money has he saved after 10 years? d) How many more years until he has saved at least twice as much as your answer from part c)?)