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 $1.00)?
A) $140,112
B) $150,360
C) $159,728
D) $182,090

Question

Quizplus · Accepted Answer

We can solve this problem using the concept of present value and perpetuity.

First, we need to find the future value (FV) of the $800 payments at the end of 20 years:
FV = $800 x [(1 + 0.14)^20 - 1] / 0.14
FV = $55,239.82

Next, we need to compound this FV for another 20 years:
FV = $55,239.82 x (1 + 0.14)^20
FV = $608,045.82

Now, we can find the present value (PV) of the perpetuity using the formula:
PV = Annual Payment / Discount Rate
PV = X / 0.14
We want to find X, which is the annual payment we will receive from the perpetuity.

Since the perpetuity starts at the end of the 41st year, we need to find the present value of the FV we calculated above at the end of the 40th year:
PV = $608,045.82 / (1 + 0.14)^20
PV = $14,867.39

Now, we can plug in the PV and discount rate to find X:
$14,867.39 = X / 0.14
X = $2,080.64

Rounding to the nearest $1.00 gives us the final answer of $159,728.

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