To buy an apartment, you borrowed on June 1, 2017 1 million euros over 5 years at 5% to be repaid in constant annual installments. As of June 19, 2017 interest rates have dropped significantly. You wonder if it is worthwhile to repay early. Your banker informs you that early repayment is accompanied by a penalty of 7% of the remaining capital

7) What would be the annual savings (in current dollars)?

8) What would be the total savings (in present value)?

9) What is the actuarial rate of the entire loan over 15 years (i.e. borrowing first at 5% and then at 3%)? We finally decide to borrow to prepay, while keeping the same annual payment as initially. 10) How much can the term of the loan be shortened?