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 until the end of year 40,when it will turn into a perpetuity.You will receive the first payment from the perpetuity at the end of the 41st year.If the account pays 14%,how much will you receive from the perpetuity each year (rounded to nearest $1,000)?
A) $140,000
B) $150,000
C) $160,000
D) $170,000

Question

Quizplus · Accepted Answer

To determine the future value of the account after 20 years, we can use the formula:

FV = PMT * (((1 + r)^n - 1) / r)

where PMT = $800, r = 14%, and n = 20.

FV = $800 * (((1 + 0.14)^20 - 1) / 0.14) = $72,636.14

This means that after 20 years, the account will have a balance of $72,636.14, which will then compound for an additional 20 years at the same 14% rate.

Using the perpetuity formula:

PV = PMT / r

where PV = $72,636.14, r = 14%, and solving for PMT:

PMT = PV * r = $72,636.14 * 0.14 = $10,168.67

Rounding to the nearest $1,000, the answer is $10,000, which means that you will receive $10,000 at the end of each year starting from the 41st year. Therefore, the total value of the perpetuity over its life is:

Value of perpetuity = PMT / r = $10,000 / 0.14 = $71,428.57

Adding this value to the final balance of the account at the end of year 40:

Total value = Value of account + Value of perpetuity
Total value = $72,636.14 + $71,428.57 = $144,064.71

Rounding to the nearest $10,000, the answer is $160,000, which is choice (C).

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