Question

Catfish Hunter’s 1974 baseball contract with the Oakland Athletics called for half of his $100,000 salary...

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.) Using an annual effective interest rate of 3.29% (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.)

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 3.29%. 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.)

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Answer #1
Number of Times to be Compounded 11 10 9 8 7 6 5 4 3 2 1 0
Periods 1 2 3 4 5 6 7 8 9 10 11 12
Dates = Previous + 15 16-Apr 1-May 16-May 31-May 15-Jun 30-Jun 15-Jul 30-Jul 14-Aug 29-Aug 13-Sep 28-Sep
Payments 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.67 4166.63 50000
Future Value 4359.283 4341.411 4323.612 4305.886 4288.233 4270.652 4253.143 4235.706 4218.341 4201.046 4183.823 4166.63 51147.76

Rate to be applied for compounding = 9.88% / (12 * 2) = 0.4117%, because the payments are made semi-monthly and so the total periods in an year = 12 * 2 = 24. Hence, the annual rate needs to be divided by 24.

Future Value for first payment = 4166.67 * (1+0.4117%)^11 = 4359.28

Similarly, after computing all the future values, the sum of future value of all payments = $51147.76, while Hunter was getting a cheque of $50,000 only.

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