Catfish Hunter's 1974 baseball contract with the Oakland Athletics called for half of his $100,000 salary to be paid to a life insurance company of his choice for the purchase of a deferred annuity. More precisely, there were to be semi-monthly contributions in Hunter's name to the Jefferson Insurance Company with the first payment on April 16 and the final payment on September 30. We suppose that the first eleven of these were to be for $4,166.67 and the final payment was to be for four cents less. (12 $4, 166.67 = $50, 000.04.)

a. Using an annual effective interest rate of 3.14% (a rate that figures in a six-year personal loan of $120,000 that Oakland's owner Charles Finley had made to Hunter in 1969 and then promptly recalled), find the value of the specified payments to the insurance company at the scheduled time of the last payment. (Hunter wished to have such an annuity in lieu of immediate salary for tax reasons. Finley claimed that he was fulfilling the contract when he offered Hunter a $50,000 check at the end of the season. Finley's default on his contractual obligation led to Hunter's historic free agency. The New York Yankees signed Hunter to a five-year, $3,750,000 contract.)

b. Suppose that the contracted payments had been made to the insurance company from April 16, 1974 through September 30, 1974, and that they accumulated at an annual effective interest rate of 3.14%. Further suppose that Hunter had drawn a level January 1st salary for twenty years, beginning on January 1, 1980, the first January after his retirement. Find the amount of the annual salary payments. (Hunter died on September 9, 1999, so he would not have received a January 1, 2000 annuity payment.)