An insurance salesman offers you a life insurance policy with the following terms.You are to make payments at a rate of $1000 per year until age 70.If you pass away at any time, the policy will pay $150,000.Consider the payments to be made at a constant continuous rate of $1000 per year.You are 30 years old, and you have a bank account that you know will offer you 5% nominal annual interest compounded continuously for an indefinite amount of time.You could choose instead to make the $1000 payments into your bank account instead of paying for the insurance policy. If you stop these payments at age 70, just as you would stop making payments on the life insurance policy, then you would simply earn interest on the bank balance that you have accumulated to that point.If you feel that you are likely to live to be 76 years old, which is the better option?

Question

Quizplus · Accepted Answer

To determine the better option, we need to compare the future value of the bank account with the insurance payout. The future value of the bank account can be calculated using the formula for the future value of a series of payments made into an account that compounds interest continuously: $FV = P \times \frac{e^{rt} - 1}{r}$, where $P$ is the payment amount, $r$ is the interest rate, and $t$ is the time in years. Here, $P = 1000$, $r = 0.05$, and $t = 40$ years (from age 30 to 70). The future value at age 70 is then left to grow for another 6 years (until age 76) at the same interest rate, so the total future value at age 76 is $FV_{76} = FV \times e^{0.05 \times 6}$. Calculating this gives a value greater than $150,000, making the bank account the better option if you live to 76.

An Insurance Salesman Offers You a Life Insurance Policy with the Following