Smith has 960 to invest on Jan 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 Dec 31, including interest and T-bill maturity, find the value of j (assuming j <10%). The period from Jan 1 to July 1 is regarded as exactly 1/2-year and the time from Jan 1 to Dec 31 is regarded as exactly 1 year for time measurement.