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An insurer classifies 60% of its drivers as low risk and 40% as high risk. Low-risk drivers have a 5% probability of an accident in a year; high-risk drivers have a 20% probability. A randomly selected driver has an accident. Calculate the probability that this driver is high risk.
Correct answer: D - 0.73
An insurance policy has an ordinary deductible of 500 and a maximum covered loss of 5,000. Ground-up losses follow an exponential distribution with mean 2,000. Calculate the expected payment per loss.
Correct answer: D - 1,393
A machine component has a lifetime that is exponentially distributed with a mean of 5 years. The component has already operated without failure for 3 years. Calculate the probability that it operates for at least 4 more years.
Correct answer: B - 0.449
The number of claims N filed by a policyholder in a year is Poisson distributed with mean Λ. The parameter Λ varies across the population and is uniformly distributed on the interval (0, 4). Calculate Var(N) for a randomly selected policyholder.
Correct answer: C - 3.33
A system contains three independent components. Their lifetimes are exponentially distributed with means of 2, 3, and 6 years respectively. The system fails as soon as any one component fails. Calculate the expected time until the system fails.
Correct answer: D - 1.00
A 10-year bond has a face value and redemption value of 1,000 and pays annual coupons at 8%. The bond is purchased to yield 6% annually. Determine whether the bond is purchased at a premium or a discount, and calculate the price.
Correct answer: C - Premium; 1,147
A loan of 10,000 is repaid with 10 level annual payments at an annual effective interest rate of 7%. Calculate the outstanding balance immediately after the fourth payment.
Correct answer: C - 6,786
A bond has a modified duration of 6.2 and a convexity of 55. Using the second-order approximation, estimate the percentage change in the bond's price if its yield increases by 50 basis points.
Correct answer: B - −3.03%
An insurer holds a portfolio of assets against a block of liabilities. The present values and the durations of the assets and the liabilities are equal. Which additional condition must hold for the portfolio to satisfy Redington immunization?
Correct answer: C - The convexity of the assets must exceed that of the liabilities
For a fully discrete whole life insurance of 1,000 on (40), you are given that A₄₀ = 0.16 and i = 0.06. Calculate the annual net premium using the equivalence principle.
Correct answer: A - 10.78
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