Suppose Becky has her choice of $10,000 at the end of each month for life or a single prize of $1.5 million. She is 35 years old and her life expectancy is 40 more years. If she takes the $1.5 million, spends $700,000 of it, and invests the remainder at an annual rate of 7.3% compounded monthly, what monthly annuity will she receive for the next 40 years? Round your answer to the nearest cent.
A) $514.67
B) $5,146.71
C) $54,683.84
D) $1,930.02
E) $7,720.07

Question

Suppose Becky has her choice of $10,000 at the end of each month for life or a single prize of $1.5 million. She is 35 years old and her life expectancy is 40 more years. If she takes the $1.5 million, spends $700,000 of it, and invests the remainder at an annual rate of 7.3% compounded monthly, what monthly annuity will she receive for the next 40 years? Round your answer to the nearest cent. ​
A) $514.67
B) $5,146.71
C) $54,683.84
D) $1,930.02
E) $7,720.07

Quizplus · Accepted Answer

If Becky took the $10,000 monthly annuity, she would receive a total of $10,000 x 12 months x 40 years = $4,800,000 over the course of her lifetime.

If Becky took the $1.5 million lump sum and invested $800,000 at an annual rate of 7.3% compounded monthly, she would earn a monthly interest rate of (7.3%/12) = 0.6083%. To find out what the monthly annuity payment would be, we can use the present value annuity formula:

PV = (C/r)[1 - (1 + r)^(-n)],

where PV is the present value of the investment, C is the monthly annuity payment, r is the monthly interest rate, and n is the total number of months (40 years x 12 months/year = 480 months).

Solving for C, we get:

C = PV(r/[1 - (1 + r)^(-n)])

Plugging in the numbers, we get:

PV = $800,000
r = 0.6083%
n = 480 months

C = $5,146.71

Therefore, Becky would be better off taking the lump sum and investing most of it, in order to receive a higher monthly annuity payment than she would by taking the $10,000 monthly annuity.

Suppose Becky Has Her Choice of $10,000 at the End