Suppose there is a series of cashflows that lasts n + 1 periods, {at}t , 0 ≤ t ≤ n, and that is growing at constant rate g, i. e. at = (1 + g) ta0, ∀t. the discount rate is fixed at r and assume g < r. find an expression for the discounted present value of the cashflows at time 0. formally, find an expression for s = a0 + a1 1+r + + an (1+r) n

Variable rate cd’s = $90 treasury bills = $150 discount loans = $20 treasury notes = $100 fixed rate cds = $160 money market deposit accts. = $140 savings deposits = $90 fed funds borrowing = $40 variable rate mortgage loans $140 demand deposits = $40 primary reserves = $50 fixed rate loans = $210 fed funds lending = $50 equity capital = $120 a. develop a balance sheet from the above data. be sure to divide your balance sheet into rate-sensitive assets and liabilities as we did in class and in the examples. b. perform a standard gap analysis and a duration analysis using the above data if you have a 1.15% decrease in interest rates and an average duration of assets of 5.4 years and an average duration of liabilities of 3.8 years. c. indicate if this bank will remain solvent after the valuation changes. if so, indicate the new level of equity capital after the valuation changes. if not, indicate the amount of the shortage in equity capital.