Kindly include all the formulas you use to solve each question.

4) (10 marks) Use the text (supplementary course package) shortcut tables for this question A person aged 30 won a cash for life lottery. The lottery pays out the money as a whole life annuity due with the following payments: $72,000 annually for the first 15 years (i.e. first 15 payments) $36,000 annually for the next 5 years $54,000 annually thereafter a) (4 marks) Using equation of value techniques, set up an equation that could be used to solve for the NSP of this annuity using (i) the blocking method and then (ii) the stacking method (no calculations required for (a)). b) (6 marks) Now instead of annual payments, assume the lottery pays out the following monthly payments: $6,000 monthly (at the beginning of each month) for the first 15 years $3,000 monthly (at the beginning of each month) for the next next 5 years $4,500 monthly (at the beginning of each month) thereafter . Using the stacking method, calculate the NSP of this annuity. 4) (10 marks) Use the text (supplementary course package) shortcut tables for this question A person aged 30 won a cash for life lottery. The lottery pays out the money as a whole life annuity due with the following payments: $72,000 annually for the first 15 years (i.e. first 15 payments) $36,000 annually for the next 5 years $54,000 annually thereafter a) (4 marks) Using equation of value techniques, set up an equation that could be used to solve for the NSP of this annuity using (i) the blocking method and then (ii) the stacking method (no calculations required for (a)). b) (6 marks) Now instead of annual payments, assume the lottery pays out the following monthly payments: $6,000 monthly (at the beginning of each month) for the first 15 years $3,000 monthly (at the beginning of each month) for the next next 5 years $4,500 monthly (at the beginning of each month) thereafter . Using the stacking method, calculate the NSP of this annuity