Question 2 A life assurance company issues a 20-year term, insurance policy to a life aged 40, with sum insured £100,000 payable immediately on death. Level premiums are payable monthly in advance throughout the term. The commissions are 10% of each premium payment (incurred at the premium payment times). Mortality follows AM92 ultimate life table with uniform distribution of deaths (UDD) assumption between integer years. Interest is i = 6% per annum. (a) Write down an expression for the gross loss at issue random variable. (b) Write down the equation of value for this policy. (c) Calculate the gross monthly premium.

On the basis of how long he has until retirement and his comfort with investment risk, Connor has decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 15% to fixed income, and 15% to cash.  If Connor assumes that each asset class provides the low end of the rates of return shown in the table below, what overall rate of return would he expect to earn over the long term?   Asset Class Degree of Risk Historical Average Rate of Return Equities High 8% - 12% Fixed Income Moderate 4% - 7% Cash Minimal 2% - 5% Group of answer choices 4.34% 6.50% 1.43% 7.25%

Table 1: Accumulated Interest Year 1 Lower-Risk Customer Higher-Risk Customer ACCUMULATED INTEREST Figure 1: Accumulated Interest 14,000.00 12,000.00 10,000.00 8,000.00 6,000.00 4,000.00 2,000.00 0 1 1,396.55 2,605.48 2 3,190.68 3,190.68 6,096.38 8,628.07 10,668.88 1,396.55 Accumulated Interest 2 6,096.38 Ⓒ2,605.48 3 Lower-Risk Customer 3,602.39 4,359.66 4,846.10 3 8,628.07 4 3,602.39 YEAR Ⓒ10,668.88 Ⓒ4,359.66 Higher-Risk Customer 5 Ⓒ12,065.44 5 Ⓒ4,846.10 12,065.44 12,616.45 5,026.46 6 6 Ⓒ12,616.45 5,026.46 4) Using the graph in 3), calculate the difference in the accumulated interest amount earned in year 5 by the credit card company charging 27.5 % versus 12.3% nominal annual rate of interest. 7

Calculate the periodic rate of interest and total number of periods in each case:   12% p.a. compounded monthly for 38 months. 5% p.a. compounded quarterly for 30 months. 8% p.a. compounded semi-annually for 2 years and 8 months. 5% p.a. compounded daily for 2 years and 10 months and 12 days.