(8) A n-year annuity-immediate pays P at the end of year 1,P+Q at the end of year 2,P+2Q at the end of year 3 , and so on. Show that the present value of this annuity is Pan+Q[iannvn] (9) Will invests 1000 at the end of each year for 10 years. Mike also invests in a 10-year annuity such that 500 is paid at the end of the first years and each subsequent annual payment is increased by 50 . If the effective annual interest rate is 3%, find the difference between the present of values of Will's annuity and Mike's annuity. (10) A 30-year annuity-immediate pays 20,000 in the first year. Thereafter, each payment is decreased by 100 each year. If i=5%, what is the present value of this annuity? (11) You invest 100 into an account at the end of the first year. Each subsequent payment is increased by 10 each year until the total payment increases to 400 . Thereafter, 400 is paid annually forever. What is a the present value of this annuity? (8) A n-year annuity-immediate pays P at the end of year 1,P+Q at the end of year 2,P+2Q at the end of year 3 , and so on. Show that the present value of this annuity is Pan+Q[iannvn] (9) Will invests 1000 at the end of each year for 10 years. Mike also invests in a 10-year annuity such that 500 is paid at the end of the first years and each subsequent annual payment is increased by 50 . If the effective annual interest rate is 3%, find the difference between the present of values of Will's annuity and Mike's annuity. (10) A 30-year annuity-immediate pays 20,000 in the first year. Thereafter, each payment is decreased by 100 each year. If i=5%, what is the present value of this annuity? (11) You invest 100 into an account at the end of the first year. Each subsequent payment is increased by 10 each year until the total payment increases to 400 . Thereafter, 400 is paid annually forever. What is a the present value of this annuity