A bank has two assets: Loan A and Loan B. Those loans are similar to simple bonds, they only give one payment Loan Payment amount Payment in Interest rate 5% $1102.5 $525 A 1 year 2 years 5% (a) You know the interest rates and the repayment amounts for the two loans. What were the principals for Loan A and Loan B (money that the bank originally lent)? Note that the principals are also the present value (ie, the market value) of the loans (b) Calculate the duration of the bank's assets (c) Suddenly and without warning, the 1-year and the 2-year interest rates both increase to 6%1. Calculate the new present values of the loans (d) By how much did the value of the assets of the bank decrease because of the increase in the interest rates? Calculate change in $ and in % (e) You may be wondering why duration is a useful concept. Here is a useful formula that allows to quickly evaluate exposure to interest rate risk: change in i in % points % change in present value of assets -duration x 1 Verify that this formula is correct: plug in the change in the interest rate and the duration you found in a)-b) and compare
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