An insurance company plans to sell annuities to investors.Based on actuarial calculations,an investor has a 20 year life span and they want a $50,000 per year annuity,payable at the end of each year.If the insurance company uses a 3% assumed investment rate,how much should the annuity cost?

Question

Quizplus · Accepted Answer

The cost of the annuity can be calculated using the present value of an annuity formula, which is:

PV = A * (1 - (1 + r)^(-n)) / r

Where PV is the present value of the annuity, A is the annual payment, r is the assumed investment rate, and n is the number of periods (in this case, 20 years).

Substituting the given values, we get:

PV = 50,000 * (1 - (1 + 0.03)^(-20)) / 0.03
PV = $743,874.46

Therefore, the cost of the annuity should be $743,874. Option B is the correct choice.

An Insurance Company Plans to Sell Annuities to Investors