Question

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 each year will you receive from the perpetuity (round to nearest $1,000)?

Answer 1

This is done in three steps.

1. You pay $800 into an account at the beginning of each 20 years.

Since the payments are made at the beginning of each period, this is a future value of an annuity due problem

$83,014.73

2. The account is left to compound for an additional 20 years.

This is a future value of a single sum problem, using the answer from (1) as your present value.

$1,140,912.16

3. At the end of the 41st year you wilil begin receiving a perpetuity from the account. The interest rate is 14%. How much will you recieve each year from the perpetuity?

Multiply 14% times the answer from (2). This is how much can be taken out each year without affecting the principal.

$1,140,912.16 x 14% = $159,727.70

2.)Assuming 2 investments have equal lives, a high discount rate tends to favor:

B.) The investment with cash flow early.

The earlier the cash flow, the more interest it earns.

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