Actuarial Exam 2/FM Prep: Comparing T-Bill Options to Find a Reinvestment Rate

Financial Math for Actuarial Exam 2 (FM), Video #15. Exercise *1.5.12 in "Mathematics of Investment and Credit", Samuel A. Broverman, 6th Edition.

Exercise *1.5.12: Smith has 960 to invest on January 1. He has the following two investment options. (a) He can buy a 6-month 1000 T-bill for a purchase price of 960, and reinvest the proceeds on July 1 at a 6-month interest rate j. (b) He can buy a one-year 1000 T-bill for a purchase price of 920 and invest the remaining 40 in an account earning interest at the same effective 6-month interest rate j as in option (a). If options (a) and (b) result in the same accumulated amount on December 31, in-
cluding interest and T-bill maturity, find the value of j (assuming j is less than 10%). The period from January 1 to July 1 is regarded as exactly 1/2-year and the time from January 1 to December 31 is regarded as exactly 1 year for time measurement.

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