The attachment contains macroeconomics questions

Example 7.12 Consider a 20-year endowment insurance issued to a life aged 30. The sum insured, $100 000, is payable immediately on death, or on survival to the end of the term, whichever occurs sooner. Premiums are payable continuously at a constant rate of $2500 per year throughout the term of the policy. The policy value basis uses a constant force of interest, 3, and makes no allowance for expenses. (a) Evaluate 1312'. (b) Use Euler's method with h = 0.05 years to calculate mix\". Perform the calculations on the following basis: Survival model: Standard Select Survival Model Interest: 5 = 0.04 per year Example 7.14 Ten years ago a man now aged 40 purchased a with-profit whole life insurance. The basic sum insured, payable at the end of the year of death, was $200 000. Premiums of $1500 were payable annually for life. The policyholder now requests that the policy be changed to a with-profit endow- ment insurance with a remaining term of 20 years, with the same premium payable annually, but now for a maximum of 20 further years. The insurer uses the following basis for the calculation of policy values and policy alterations. Survival model: Standard Select Survival Model Interest: 5% per year Expenses: none Bonuses: compound reversionary bonuses at rate 1.2% per year at the start of each policy year, including the first. The insurer uses the full policy value less an expense of $1000 when calculating revised benefits. You are given that the actual bonus rate declared in each of the past 10 years has been 1.6%. (a) Calculate the revised sum insured, to which future bonuses will be added, assuming the premium now due has not been paid and the bonus now due has not been declared. (b) Calculate the revised sum insured, to which future bonuses will be added, assuming the premium now due has been paid and the bonus now due has been declared to be 1.6%