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 purchase 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? (Let P1 and P4 denote the prices of the one-year bond and of the four-year bond, respectively.

The answers: P1=$88,899.64 and P4=$177,799.27

Please show work, NO Spreadsheets