You owe Mr. Lauder $2,000 in tuition expenses due at the end of the year and you want to set up a fund to meet the obligation. The investment vehicle available to you is a 2-year zero-coupon bond earning 8.5% effective. You can also use your savings in your bank account, which offers you no interest because the principal is too small. Assume that the effective rate of interest is 8.5%.

(a) You plan to construct a fund consisting of the zero-coupon bond and bank deposit. At the time of the construction of the fund the surplus of you position is zero. How much should you invest in the zero-coupon bond to minimize the interest-rate risk?

(b) Calculate the present value of your portfolio if the effective rate of interest goes up or down by 50 basis points immediately after you start up the portfolio and compare it with the present value of the liability.

PLEASE SHOW ALL WORK BY HAND AS I AM NOT ALLOWED TO USE A FINANCE CALCULATOR OR EXCEL. THANK YOU.