An insurance company plans to sell annuities to investors.Based on actuarial calculations,an investor has a 15 year life span and they want a $30,000 per year annuity,payable at the end of each year.If the insurance company uses a 4% assumed investment rate,how much should the annuity cost?

Question

Quizplus · Accepted Answer

To calculate the cost of the annuity, we need to use the present value formula, which is:
Present Value = Annuity Payment x (1 - (1 + i)^-n) / i
Where i = assumed investment rate = 4%, n = life span = 15 years, and annuity payment = $30,000 per year.
Plugging in these values, we get:
Present Value = $30,000 x (1 - (1 + 0.04)^-15) / 0.04 = $333,552
Therefore, the cost of the annuity should be $333,552, which is option C.

An Insurance Company Plans to Sell Annuities to Investors