a. A pension fund has to pay out $750,000 to the retirees at the end of every month for the next 50 years. The fund will be earning 9.6% compounded monthly for the first 30 years and 7.2% compounded monthly for the last 20 years. In order to be able to make these payments, how much money would have to be in the pension fund now?

b. Dakota intends to save for occasional major travel holidays by contributing $275 at the end of each month to an investment plan. At the end of every three years, she will withdraw $10,000 for a major trip abroad. If the plan earns 6% compounded monthly, what will be the plan's balance after seven years?

c. If money can earn 6% compounded monthly, how much more money is required to fund an ordinary annuity paying $200 per month for 30 years than to fund the same monthly payment for 20 years?