Geraldine was injured in a car accident, and the insurance company has offered her the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum.If a fair return is 7.5%, how large must the lump sum be to leave her as well off financially as with the annuity?
A) $225,367
B) $237,229
C) $249,090
D) $261,545
E) $274,622

Question

Quizplus · Accepted Answer

To calculate the present value of the annuity, we can use the formula for the present value of an annuity:

PV = (PMT / r) x (1 - (1 + r)^-n)

where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

PV = (25,000 / 0.075) x (1 - (1 + 0.075)^-15) = $237,229.19

So, the lump sum must be equal to this amount to leave Geraldine as well off financially as with the annuity. Therefore, the best choice is B.

Geraldine Was Injured in a Car Accident, and the Insurance