10.9 An actuarial student takes out a mortgage for 250,000 with a term of 25 years. The mortgage is repayable by level instalments made monthly in arrears. Interest is charged at a rate of 6% pa effective. Liam style [2] (0) Calculate the monthly repayment. (ii) (a) Calculate the capital repaid in the fourth year. [4] (b) Calculate the interest element of the 49th repayment. After completing her exams, six years after taking out the mortgage, the newly-qualified actuary reviews her finances and realises that she can afford to make repayments at twice the rate calculated in (0) (iii) Calculate the length of time by which this course of action reduces the remaining term of the loan. [4] (iv) Calculate the amount of the final repayment, and hence the interest saved by the actuary, if she follows this course of action. [5] [Total 15)