4. You are given the following information . X is the time-value at the end of year two of all payments from a 20-year annuity-due which pays 1 per year The annual effective interest rate for year tis_ 8+t Which of the summations given below is equal to the value of X? 28 10 10 29 11 30 10 t=g 10 11 Answer: 5. A 39-year annuity-immediate will pay 13 in each of the first 3 years, 12 in each of the next 3 years, and so on, until payments of 1 are made in each of the last 3 years. The present value of the annuity at an annual effective interest rate of 3% is X. Determine X (a) 59 (b) 165 (c) 177 (d) 184 (e) 187 Answer 6. At an annual effective rate of interest i> 0, payments of 100 now, 200 two years from now and 100 four years from now have a total present value of 300. Calculate i (a) 11.7% (b) 13.0% (c) 14.5% (d) 15.8% (e) 16.9% Answer: 7. A perpetuity pays 1 at the end of the first two years (i.e. at times t 1 and t 2), pays 2 at the end of the second two years (i.e. at times t = 3 and t = 4), 3 at the end of the third two years (i.e. at times t= 5 and t= 6), and so on Assuming an annual effective interest rate of 8%, find the present value of the perpetuity. Give nearest whole number