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Please show each mathematical step with formula and explain. thank you In a very simplistic example, a bank has only two positions on its balance

Please show each mathematical step with formula and explain. thank you

image text in transcribedimage text in transcribed In a very simplistic example, a bank has only two positions on its balance sheet: - On the asset side, there is a loan with an outstanding amount of EUR 50.000, a (remaining) maturity of 9 months (or 270 days) and an interest rate of 1.5% (fixed). - On the liabilities side, there is a EUR 50.000 cash deposit with a maturity of 1 month (or 30 days) at an interest rate of 0.125% (fixed). c) The Ioan contract offers an early redemption option to the client, i.e. the client is allowed to repay the loan before contractual maturity (on short notice). In six months from now, the client "suddenly" decide to repay the loan in full, i.e. repayment takes place three months before maturity. Obviously, the hedge in a) and the matched book in b) do not work anymore. What should the bank do now in a) and in b), respectively

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