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The Dakota Bank makes five year loans for college students. Dakota wants to receive an annual interest rate 3.2% compounded continuously without taking into account defaults and inflation. Dakota knows that inflation for the next five years will be at an annual rate of 2.4% compounded continuously.
College students have a high default rate. Dakota believes that 4.2% of the students will default on the loan at the end of 5 years. She also believes that she will be able to recover 20% of the amount owed on defaults.
a. Calculate the credit spread that Dakota needs to charge as an annual rate compounded continuously. (Enter answer as a decimal and round to the nearest 5 decimal places.)
b. Calculate the total annual interest rate compounded continuously that Dakota should charge for the loans including the components for default and inflation. (Enter answer as a decimal and round to the nearest 5 decimal places.)
c. Sammie borrows 32,000 from Dakota to be repaid at the end of five years. Calculate the amount that Sammie will need to repay at the end of five years. (Enter answer as a decimal and round to the nearest 2 decimal places.)
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