A life insurance company issues a Type B universal life policy to a life
age 60. The main features of the contract are as follows.
Premiums: 3,000 per year, payable yearly in advance.
Expense charges: 4% of the first premium and 1% of subsequent premiums.
Death benefit: 10,000 plus the Account Value, payable at the end of the year
of death.
Cost of insurance rate: 0.022 for 60 x 64; discounted at 3% to start of policy year.
Cash surrender values: 90% of the account value for surrenders after 2 or 3
years, 100% of the account value for surrenders after four years or more.
The company uses the following assumptions in carrying out a prot test of this
contract.
Interest rate: 6% per year
Credited interest: 5% per year.
Survival model: q60+t = 0:02 for t = 0; 1; 2; 3.
Withdrawals: None in the first three years; all contracts assumed to surrender
at the end of the fourth year.
Initial expenses: 200 pre-contract expenses.
Maintenance expenses: 50 incurred annually at each premium date including
the first.
Risk discount rate: 8% per year.
There are no reserves held other than the account value.
(a) (4 points) Show that the projected final account value for an insured surrendering at the end of the fourth year is 12,400 to the nearest 100. You should calculate the value to the nearest 1.
(b) (7 points) Calculate the prot margin for a new policy.
(c) (2 points) Calculate the NPV for a policy that is surrendered at the end of the second year.
Question:
There're 3 interest rates in this problem. It's clear that i^q=3% is used to find the CoI value. However, "interest rate" (which I call i) and "credited interest rate" (which I call i^c) are kind of confusing.
The SOA solution uses "i^c" to establish the AV's and "i" to profit test. Is it the common practice? Thanks!
age 60. The main features of the contract are as follows.
Premiums: 3,000 per year, payable yearly in advance.
Expense charges: 4% of the first premium and 1% of subsequent premiums.
Death benefit: 10,000 plus the Account Value, payable at the end of the year
of death.
Cost of insurance rate: 0.022 for 60 x 64; discounted at 3% to start of policy year.
Cash surrender values: 90% of the account value for surrenders after 2 or 3
years, 100% of the account value for surrenders after four years or more.
The company uses the following assumptions in carrying out a prot test of this
contract.
Interest rate: 6% per year
Credited interest: 5% per year.
Survival model: q60+t = 0:02 for t = 0; 1; 2; 3.
Withdrawals: None in the first three years; all contracts assumed to surrender
at the end of the fourth year.
Initial expenses: 200 pre-contract expenses.
Maintenance expenses: 50 incurred annually at each premium date including
the first.
Risk discount rate: 8% per year.
There are no reserves held other than the account value.
(a) (4 points) Show that the projected final account value for an insured surrendering at the end of the fourth year is 12,400 to the nearest 100. You should calculate the value to the nearest 1.
(b) (7 points) Calculate the prot margin for a new policy.
(c) (2 points) Calculate the NPV for a policy that is surrendered at the end of the second year.
Question:
There're 3 interest rates in this problem. It's clear that i^q=3% is used to find the CoI value. However, "interest rate" (which I call i) and "credited interest rate" (which I call i^c) are kind of confusing.
The SOA solution uses "i^c" to establish the AV's and "i" to profit test. Is it the common practice? Thanks!
SOA WA#18 Three interest rates in UL-B problem
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