# SOLUTION: Interest Rates Balance Sheets Duration & Convexity Formula Exam Practice

Attached.1. Assume the interest rate on a 90-day, \$1 million face value, T-Bill is currently selling at adiscount rate of 3.80%.a. What will be the price of T-Bill today? What is the holding period return of the TBill?days to maturity ∗ Interest ratePrice today = Face value −accounting daysPrice Today = \$100 −90 ∗ 3.80%= \$100 − \$0.95360Price today = \$99.05 ∗ 100Price today = \$990,500Holding period return = (\$1,000,000 − \$990,500 = \$𝟗, 𝟓𝟎𝟎b. Assume a borrower is given the following options for payment on \$1,000,000 loan.Show payment for all three options.i.10-year amortization loan paying annual interest rate of 12%.Monthly interest rate = 12%/12 = 1%Duration = 12 *10-years = 120 monthsii.Monthly payments =Pv ∗ r(1 − (1 + r)tMonthly payments =\$1,000,000 ∗ 1%= \$14,3471 − (1 + 1%)−12010-year non-amortization loan with principal payment with principal paymentof at maturity payment paying annual interest rate of 12%Monthly interest rate = 12%/12 = 1%Monthly payments = 1% *\$1,000,000 = \$10,000Month PMTBalance1\$10,000\$1,000,0002\$10,000\$1,000,0003\$10,000\$1,000,000120\$1,010,000 \$0iii.He will pay a monthly payment of \$10,000 and \$1,010,000 on the last month10-year loan with no interest or principal payment for 1-5 and then 5 equalpayments from years 6-10. Interest will continue to accrue during period 1-5wen no payments are being made.1-5 years:𝐹𝑉 = 𝑃(1 + 𝑟)𝑛𝐹𝑉 = \$1,000,000(1 + 1%)60𝐹𝑉 = \$1,816,696.70Year 6-10At the beginning of year 6 the loan will be worth \$1,816,696.70𝐹𝑉 = 𝑃(1 + 𝑟)𝑛𝐹𝑉 = \$1,816,696.70(1 + 1%)60𝐹𝑉 = \$3,300,386.90Equal payments:𝐴𝑛𝑢𝑎𝑙 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 = =\$3,300,386.90= \$𝟔𝟔𝟎, 𝟎𝟕𝟕. 𝟑𝟖5c. Distinguish between competitive and non-competitive bids when purchasing Treasurybonds in the U.S.A non-competitive bid is made by small investors to purchase Treasury bonds while acompetitive bid is made by large investors to purchase U.S. Treasury bonds.2. Assume a bank has the folliwng balance sheet (in 000s).a. Determine the 6-month and 1-year cumulative GAP. What is the impact on netincome (NII), if interest rates are expected to increase by 1% across the board (allinterest rates)?Reciprocal bucket Assets Liabilities GAP Cumulative GAP1 to 6 months\$400\$200\$200\$2006 to 12 months\$400-\$400-\$200If the interest rates increase by 1% the net income will decrease by \$2,000 (-200,000x 1%).b. What is the impact on net interest income (NII), if the interest rates are expected toincrease as specified in the potential rate change for the 6-month and 1-year CGAPs.Reciprocal bucket Assets RateLiabilities RateGAPS1 to 6 months\$4001% \$4\$2000.25% \$0.5 \$3.56 to 12 months\$4000.75% \$3-\$30.5Net interest income will increase by \$500.c. Explain the difference b…

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