2. [15 marks] For the scenario described below, calculate the profit signature, the discounted payback period and the net present value, using a hurdle interest rate of 10% per year effective for the policy described in question 1. Policy remained inforce for 15 years Premiums of $3500 are paid for 5 years and no premiums are paid thereafter The Col rates and expense charges are unchanged from question 1 The face amount is unchanged The insurer has earned 9.25% each year on their funds The credited interest rate (and rate used for discounting COI amounts) for the UL account value is calculated using a spread approach. The insurer keeps the first 2.5% and pays the remainder to the policyholder. Actual mortality was 80% of the Stats Canada rates Incurred expenses were $1000 at inception plus $85 plus 6.5% of premium each year There was a cost of surrender of $40 even if there was no cash value paid out, and a death expense of $150. Surrenders occur at year end with probability of 5% in year 1 then increasing by 5% each year to year 14 and jumping to 100% in year 15. The insurer holds the full account value as a reserve for this contract. Universal Life 1. [10 marks] A Universal Life policy is sold to a 35-year old woman. The initial premium is $3500 and the face amount is $200,000. The policy provides a death benefit of the face amount plus the account value i.e. an increasing death benefit policy. The cost of insurance rates is equivalent to the Stats Canada 2009-2011 - Canada female rates and the effective rate of interest used for discounting COI amounts is 6%. The expense charges are 5% of the premium plus $65. Surrender charges decrease over time and never exceed the account value. The surrender charge schedule is as follows: 1 2 3-5 6-10 11-15 16+ Policy year Surrender Charge $5000 $4500 $4000 $2500 $1000 Assume the policy remains inforce for 15 years, the credited interest rate is 6%, all cash flows occur at policy anniversaries. Project the account value and the cash value at each year end for the 15-year projected term, given that the policyholder pays a premium of $3500 for 5 years then stops paying premiums. 2. [15 marks] For the scenario described below, calculate the profit signature, the discounted payback period and the net present value, using a hurdle interest rate of 10% per year effective for the policy described in question 1. Policy remained inforce for 15 years Premiums of $3500 are paid for 5 years and no premiums are paid thereafter The Col rates and expense charges are unchanged from question 1 The face amount is unchanged The insurer has earned 9.25% each year on their funds The credited interest rate (and rate used for discounting COI amounts) for the UL account value is calculated using a spread approach. The insurer keeps the first 2.5% and pays the remainder to the policyholder. Actual mortality was 80% of the Stats Canada rates Incurred expenses were $1000 at inception plus $85 plus 6.5% of premium each year There was a cost of surrender of $40 even if there was no cash value paid out, and a death expense of $150. Surrenders occur at year end with probability of 5% in year 1 then increasing by 5% each year to year 14 and jumping to 100% in year 15. The insurer holds the full account value as a reserve for this contract. Universal Life 1. [10 marks] A Universal Life policy is sold to a 35-year old woman. The initial premium is $3500 and the face amount is $200,000. The policy provides a death benefit of the face amount plus the account value i.e. an increasing death benefit policy. The cost of insurance rates is equivalent to the Stats Canada 2009-2011 - Canada female rates and the effective rate of interest used for discounting COI amounts is 6%. The expense charges are 5% of the premium plus $65. Surrender charges decrease over time and never exceed the account value. The surrender charge schedule is as follows: 1 2 3-5 6-10 11-15 16+ Policy year Surrender Charge $5000 $4500 $4000 $2500 $1000 Assume the policy remains inforce for 15 years, the credited interest rate is 6%, all cash flows occur at policy anniversaries. Project the account value and the cash value at each year end for the 15-year projected term, given that the policyholder pays a premium of $3500 for 5 years then stops paying premiums