Confusion in Pricing T-Bill one, methods, interest, discount, face

lxwarr30

Why can not we price the t-bill using the present value formula and get the same answer as by applying the discount on the face value and then subtracting it from the face value?

E.g. $100,000 tbill pays 5% in interest with one month remaining to maturity

Book's method:
Purchase price = $100,000 - [ .05 x (1/12) x ($100,000) ] = $995,833.33

Present value method:
Purchase Price = $100,000 / [ 1 + 0.05 x (1/12) ] ^ 1 = $99,585.06

Why both these methods are not giving the same answers?