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# Maria had received a huge number of parking tickets over a 15-year period but didn't bother to pay any of them. She owes the local municipality...

Maria had received a huge number of parking tickets over a 15-year period but didn't bother to pay any of them. She owes the local municipality 25,088.51 euros in unpaid parking tickets and 22,142.85 euros in late payment fees. To enforce payments of outstanding debt, local municipalities have coordinated with the central government and managed to freeze the assets of citizens with such debt. Recently, the government oered the possibility of restructuring such debt according to the following rules: (i) Plan A: if 2 to 24 monthly payments of equal value are arranged, then 80% of the late payment fees is forgiven; (ii) Plan B: if 25 to 48 monthly payments of equal value are arranged, then 70% of the late payment fees is forgiven; (iii) Plan C: if 49 to 72 monthly payments of equal value are arranged, then 60% of the late payment fees is forgiven; and (iv) Plan D: if 73 to 100 monthly payments of equal value are arranged, then 50% of the late payment fees is forgiven. In each case, the amount of monthly payment is determined so that the balance is completely paid o when the last payment is made. Maria's son, Jorge, oers to bail her mother out by providing 34,000 euros in cash. At the same time, Jorge teaches his mother the basics of time value of money and discounting.

1. Suppose that Maria can use the cash she received from Jorge to oer a loan, up to 34,000 euros, to Manuel, a local small business owner who wants to expand his

business. Manuel agrees to pay back in monthly installments, of equal value, based on a quarterly APR of 3%. The loan amount and number of monthly payments made by Manuel is to be chosen by Maria. What is the optimal plan that Maria should follow to pay o her debt? [You need to specify the exact number of monthly payments to the local municipality and the exact monthly payment amount.]

2. How would Maria's optimal plan change if Manuel oered a 7% monthly APR? [Again, you need to specify the exact number of monthly payments to the local municipality and the exact monthly payment amount.]