An insurance company is required to pay an annuity annually in advance for 4 years. The first payment is $1.5 million and each subsequent payment is 3% greater than the previous one. (i) Calculate, showing all working and using an effective rate of interest of 8% p.a., the convexity of the annuity. The company is considering investing in a single zero-coupon bond of suitable term to cover the present value of the annuity. (ii) Explain if it is possible to find a zero-coupon bond such that the fund would be immunised against small changes in the rate of interest.