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.

1) Calculate the amount of the annual instalments.

2) If these were monthly payments (and not annuities), for a rate of 5% (APR), what would be the amount?

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

3) Calculate the remaining capital according to the annual payment in 2021.

4) How much do you need to borrow to prepay (including the penalty)

5) What is the interest rate at which early repayment would be interesting? You are offered a constant annuity loan at 3% to prepay the previous loan (and pay the penalty).

6) What would be the amount of the new annuity?

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?