P26-29A Using the time value of money You are planning for a very early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw $215,000 per year for the next 40 years (based on family history, you think you will live to age 80). You plan to save by making 10 equal annual installments (from age 30 to age 40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money in this fund until it is completely depleted when you are 80 years old. Requirements 1. How much money must you accumulate by retirement to make your plan work

Amount of money to be accumulated by retirement = $2,102,485

Explanation:

First we understand that what we are dealing with in this question is referred to as the Time value of Money. The time value of money is usually represented as either the present value or the future value of money.

In order to calculate the answer to the question, we use the present value and find the present value of the $215,000 to be withdrawn per year for 40 years.

We make use of the table on the Present Value Annuity factor as well.

Step 1:

Annual amount to be withdrawn is $215,000

The yearly rate of interest 10%

The period or number of years = 40 years

Using the Present Value Annuity factor table, we find the figures for (i = 10%, n = 40 years). We get 9.779

Therefore, the present value that will allow us withdraw $215,000 for the next 40 years

= $215,000 x 9.779

= $2,102,485

This is the amount of money to be accumulated by retirement.