Chapter 3: Insurance Companies and Pension Funds
3.16. (Spreadsheet Provided).
Use Table 3.1 to calculate the minimum premium an insurance company should charge for a $5
million three-year term life insurance contract issued to a man aged 60. Assume that the
premium is paid at the beginning of each year and death always takes place halfway through a
year. The risk-free interest rate is 6% per annum (with semiannual compounding).
The unconditional probability of the man dying in years one, two, and three can be calculated
from Table 3.1 as follows:
Year 1: 0.011046
Year 0: 1
The present value of the premiums received per dollar of premium paid per year is therefore
2.800458. The minimum premium is
83.427,57
800458.2
20.824,160
or $57,427.83.
3.17
An insurance company’s losses of a particular type per year are to a reasonable approximation
normally distributed with a mean of $150 million and a standard deviation of $50 million.
(Assume that the risks taken on by the insurance company are entirely non-systematic.) The
one-year risk-free rate is 5% per annum with annual compounding. Estimate the cost of the
following:
(a) A contract that will pay in one-year’s time 60% of the insurance company’s costs on a pro
rata basis
(b) A contract that pays $100 million in one-year’s time if losses exceed $200 million.
(a) The losses in millions of dollars are normally distributed with mean 150 and standard
The salary of the employee makes no difference to the answer. (This is because it has the effect
The spreadsheet is used in conjunction with Solver to show that the required contribution rate is