Providence Health Care is obligated to make a payment of $300,000 in exactly three years. In order to provide for this obligation, their financial officer decides to purchae a combination of one-year zero-coupon bonds and four-year zero-coupon bonds. Each of these is sold to yield an annual effective yield of 4%. How much of each type of bond should be purchased so that the present value and duration conditions of Redington immunization are satisfied? Is the convexity condition also satisfied at i = 4%?

The answer in the back of the book says: $88,899.64 of one-year bond, $177,799.27 of four-year bond; yes.

But whats the process of getting this answer using the appropriate formulas?