Question

You would like to have enough money saved after your retirement such that you and your heirs can receive $100,000 per year in perpetuity. How much would you need to have saved at the time of your retirement in order to achieve this goal

Answer 1

Answer:

The amount you need to have saved at the time of your retirement in order to achieve this goal is $800,000.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

You would like to have enough money saved after your retirement such that you and your heirs can receive $100,000 per year in perpetuity. How much would you need to have saved at the time of your retirement in order to achieve this goal? (Assuming that the perpetuity payment starts one year after the date of your retirement. The annual interest rate is 12.5 percent).

The explanation to the answer is now given as follows:

A perpetuity can be described as periodic payments that are receivable or payable indefinitely or forever. A perpetuity is also referred to as an annuity that does have an end.

In order to determine the amount you need to have saved at the time of your retirement in order to achieve the goal, the formula for calculating the present value (PV) of a perpetuity is used as follows:

PV = FV / r ............................................. (1)

Where;

PV = Present value of or the amount needed to be saved at the time of retirement = ?

FV = Future value of the amount you and your heirs can receive = $100,000

r = interest rate = 12.5%

Substituting the values into equation (1), we have:

FV = $100,000 / 12.5%

FV = $800,000

Therefore, the amount you need to have saved at the time of your retirement in order to achieve this goal is $800,000.