Question

help with
purchase price of 26 wk t bill with a maturity value of $1000 earns an annual interest rate of 5.25%

Answer 1

It's a 6-mo. Tbill, so the annual interest is 1/2(.0525), and the maturity value is 1000. So you're looking for the number x that will equal 1000 in six months.
The usual estimation for continuously compounded interest is X*e^Rt so plug in the values:
x*e^1/2(.0525)=1000