An insurance company offers you an end of year annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9 percent. What should you be willing to pay today for this annuity?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to calculate what we should be willing to pay today:
PV = C * [(1 - (1 + r)^-n) / r]
Where PV is the present value, C is the annual payment, r is the interest rate, and n is the number of years.
In this case, we have:
PV = $48,000 * [(1 - (1 + 0.09)^-20) / 0.09]
PV = $438,144
So we should be willing to pay $438,144 today for this annuity. The closest answer choice is B.

An Insurance Company Offers You an End of Year Annuity