You are going to pay $800 into an account at the beginning of each of 20 years.The account will then be left to compound for an additional 20 years.At the end of the 41st year you will begin receiving a perpetuity from the account.If the account pays 14%,how much will you receive each year from the perpetuity (round to nearest $1,000)?
A)$140,000
B)$150,000
C)$160,000
D)$170,000

Question

Quizplus · Accepted Answer

Using the formula for the future value of an annuity due, we can find the value of the account after 20 years of deposits:

FV = (PMT x ((1 + r)^n - 1) / r) x (1 + r)
FV = ($800 x ((1 + 0.14)^20 - 1) / 0.14) x 1.14
FV = $60,674.13

This is the amount in the account at the end of the 20-year deposit period. We can then leave this amount to compound for another 20 years to get:

FV = $60,674.13 x (1 + 0.14)^20
FV = $1,058,167.26

Finally, we can find the perpetuity payment using the formula:

Perpetuity payment = PV x r
Perpetuity payment = $1,058,167.26 x 0.14
Perpetuity payment = $148,152.22

Rounding to the nearest $1,000, the answer is $160,000 (Choice C).

You Are Going to Pay $800 into an Account at the Beginning