3. A loan is to be repaid by level annual instalments of 6,000 at the end of each of the next 12 years. The amount of principal repaid in the 10th instalment is 4 times the interest in the 7th instalment. (a) Determine the interest rate i of the loan. (b) Immediately after the 7th instalment, the borrower wants to shorten the term of the loan by 2 years so that the 10th instalment will be the last. The next 3 instalments will still be level. The lender agrees, but requests either of the following: the interest rate be increased to i + 0.01, or an explicit prepayment penalty of 600 be added to the outstanding balance, with the same rate i as before. Option 1: Option 2: Which option should the borrower take? 1 [6+4 = 10 marks]