46. Mark receives 500,000 at his retirement. He invests 500,000-X in an annual payment 10-year annuity-immediate and X in an annual payment perpetuity- immediate. His total annual payments received during the first 10 years are twice as large as those received thereafter. The annual effective rate of interest is 6%. Calculate X. Answer: 346,835.59 47. At a nominal rate of interest i, convertible semiannually, the present value of a series of payments of 1 at the end of every 2 years, forever, is 5.89. Calculate i. Answer: i = 7.99648% 48. Annuities X and Y provide the following payments: End of year Annuity X Annuity Y 1-10 K 11-20 21-30 K Annuities X and Y have equal present values at an effective anmal interest rate i such that ylo - 1/2. Determine K. Answer: K - 9/5