STA 2191: FINANCIAL MATHEMATICS I CAT I 25th June 2013 (11.00 A.M) 1. At what simple rate of interest will KSh.5,000 accumulate to KSh.8,200 in 4.5 years? [2 marks] 2. In how many years will KSh.5,000 accumulate to KSh.7,500 assuming a simple rate of discount of 6%. [2 marks] [5 marks] 3. If (3) 12%, calculate (5) and d(4). 4. A deposit of X is made into a fund which pays an annual effective interest rate of 6% for 10 X years. At the same time, is deposited into another fund which pays an annual effective rate 2 of discount of d for 10 years. The amounts of interest earned over the 10 years are equal for both funds. Calculate d. [3 marks] 5. At an effective annual interest rate of i, a payment of 121 now (immediately) and another 121 at the end of the year has the same present value as a payment of 169 at the end of two years and another 169 at the end of three years. Calculate the present value of these two cash flows [3 marks] 6. At time 0, K is deposited into Fund X, which accumulates at a force of interest 8(t) = 0.006t. At time m, 2K is deposited into Fund Y, which accumulates at an annual effective interest rate of 10%. At time n, where n> m, the accumulated value of each fund is 4K. Determine m. [6 marks] 7. The force of interest 8(t) is a function of time and at any time t, measured in years, is given by the formula: 8(t) = 0.04 0.008t 0.005 +0.0003t 8. Show that am = 9. If am 5 and sm= 15 find i. 0 10 (a) Calculate the present value of a unit sum of money due at time t = 12. (b) Calculate the equivalent effective annual rate of interest over the 12 years. (c) Calculate the value at time t = 0 of a continuous payment stream that is paid of e-0.05 per unit time between time t = 2 and time t = 5. 1-v"h [5 marks] [1 marks] at the rate [3 marks] [4 marks] [6 marks]