An insurance company issued a $90 million 1-year note at 8 per cent add on annual interest (paying one coupon at the end of the year) and used the proceeds to fund a $100 million face value 2-year commercial loan at 10 per cent annual interest. Immediately after these transactions were (simultaneously) undertaken, all interest rates went up 150 basis points.

a. Use the duration model to estimate the change in the value of the loan due to the increase in the interest rate.

b. Find the exact change in the value of the loan using the valuation formula.

c. Contrast the results obtained in (a) and (b). There is obviously a difference in the results. Explain what makes this difference and how the difference can be corrected. Show all workings and calculations.