OLBk+m = Bonus Problem 1 (Optional, 25 marks) (a) A loan of amount L is repaid by n payments made at times t, t2, ..., tn. We let Pk be the amount of kth repayment. We let OLBk be the outstanding balance just after kth repayment. By considering the relation between OLBk-1 and OLBk, Show that for any non-negative integers k and m, we have Future value of SFuture value of repayments (OLBk at time tk+m) made between tk and tk+m (b) A person borrows an amount of $120000. He agrees to repay the loan by m level quarterly regular payment with amount $X each plus 1 balloon payment to be paid 3 months after the mth repayment. It is also given that the loan charges compound interest at a quarterly effective interest rate i > 0. You are given that The outstanding balance at kth repayment date is OLBK = 59471.358. The outstanding balance at (k + 4) th repayment date is OLBk+4 = 49865.692. The outstanding balance at (k + 12)th repayment date is OLBk+12 = 27559.263. (* Here, k + 12 0. You are given that The outstanding balance at kth repayment date is OLBK = 59471.358. The outstanding balance at (k + 4) th repayment date is OLBk+4 = 49865.692. The outstanding balance at (k + 12)th repayment date is OLBk+12 = 27559.263. (* Here, k + 12