Answer Happy

5. [14 marks] (a) [9 marks] A loan of €7,000 is being repaid by payments of €500 at the end of each quarter for as long as necessary, plus a smaller final payment. The nominal rate of interest converted quarterly is 12%. Find (i) the number of payments that will be necessary; (ii) the size of the final payment; (iii) the total of the payments; (iv) the outstanding loan balance after the fifth payment; (v) the interest paid and the amount by which the principal is reduced in the sixth payment. (b) [5 marks] Let n be a non-negative number and let 3 denote the accumulated value at time n of an annuity of €1 per unit time payable continuously between 0 and time n. Show that Sm (1+i)" - 1 In(1 + i) =