8. The lifetime of a certain breed of animal follows the function:- 1x = lo (25 x)2 for 0 Sxs 25. ^ 625 1 (a) Using lo = 100,000, build columns on your spreadsheet for x, lx, dx, qx, Roxo exu Be sure to round lis to the nearest whole number before calculating the other columns (EXCEL has a ROUND function to help you do this). Include a graph for the lx values. Display the qx and Px values to 5-decimal points and the x values to 2-decimal point. (5 marks) e (b) You wish to design an annuity product that pays the owner of the animal $R a month to help pay for supplies needed to care for the animal (as long as the animal is alive). If you plan to charge each customer a net single premium of $1500 to buy one of these annuities when the animal has just turned age x, how much would you charge? Use ji = 3.5%. (hint: set up a table with values of z for x = 0, 1, 2, ..., 2linthen calculate the monthly benefit) (4 marks) (c) You also wish to design a whole life insurance policy that pays $10,000 to the owner of the animal upon the death of the animal. Calculate the net single premium that you would charge a customer who bought a policy when their animal was age x, where x = 0, 1, 2, ..., 20. Use ji = 3.5%. (4 marks) 8. The lifetime of a certain breed of animal follows the function:- 1x = lo (25 x)2 for 0 Sxs 25. ^ 625 1 (a) Using lo = 100,000, build columns on your spreadsheet for x, lx, dx, qx, Roxo exu Be sure to round lis to the nearest whole number before calculating the other columns (EXCEL has a ROUND function to help you do this). Include a graph for the lx values. Display the qx and Px values to 5-decimal points and the x values to 2-decimal point. (5 marks) e (b) You wish to design an annuity product that pays the owner of the animal $R a month to help pay for supplies needed to care for the animal (as long as the animal is alive). If you plan to charge each customer a net single premium of $1500 to buy one of these annuities when the animal has just turned age x, how much would you charge? Use ji = 3.5%. (hint: set up a table with values of z for x = 0, 1, 2, ..., 2linthen calculate the monthly benefit) (4 marks) (c) You also wish to design a whole life insurance policy that pays $10,000 to the owner of the animal upon the death of the animal. Calculate the net single premium that you would charge a customer who bought a policy when their animal was age x, where x = 0, 1, 2, ..., 20. Use ji = 3.5%. (4 marks)