1. Suppose a 60-year-old person wants to purchase an annuity from an insurance company that would pay $50,000 per year until the end of that person’s life. The insurance company expects that this person would live for 25 more years and it would be willing to pay 5.3 percent on the annuity. How much should the insurance company ask this person to pay for the annuity?
2. You deposit $7500 annually into a life insurance fund for the next 20 years, at which time you plan to retire. Instead of a lump sum, you wish to receive annuities for the next 20 years. What is the annual payment you expect to receive beginning in year 21 if you assume an interest rate of 7 percent for the whole time period?
3. Suppose the loss ratio on a line of property insurance is 72 percent, the expense ratio is 26 percent, the dividend ratio is 3 percent, and the investment yield is 6 percent. How profitable is this line?
4. An insurance company’s projected loss ratio is 80 percent, its loss adjustment expense ratio is 18 percent, and the dividend ratio is 3 percent. What is the minimum investment yield the company requires to earn a 4% profit?