An insurance company must make a payment of $19,487.17 in 7 years. The market interest rate is 10%, which means the present value of the obligation is $10,000. The company's risk manager wishes to reduce interest rate risk of this obligation using two types of assets: 3-year zero-coupon bonds (to be referred to as zeros below) and perpetuities (which pays annual coupons). Both the zero and the perpetuity yield 10% per year. How can the manager immunize the obligation? That is, how many zeros and perpetuities should this manager buy to achieve immunization? (For simplicity, assume the manager can buy fractional units of bonds and perpetuities.) Note: duration of a perpetuity is 1+ytm ytm