Suppose a man is 30years old and would like to retire at age 65 Furthermore, he would like to have a retirement fund from which he can draw an income of $50,000 per yearlong dash—forever! How can he do it? Assume a constant APR of 5%.
He can have a retirement fund from which he can draw $50,000 per year by having $ in his savings account when he retires.
Suppose a man is 35 years old and would like to retire at age 60. Furthermore, he would like to have a retirement fund from which he can draw income of $125,000 per year— forever! How can he do it? Assume a constant APR of 8%.
To determine the amount of money the man needs to have in his savings account when he retires to be able to draw $50,000 per year indefinitely, we can use the concept of a perpetuity formula. A perpetuity is an infinite series of cash flows that continues forever.
The formula to calculate the present value of a perpetuity is as follows:
PV = PMT / r
Where:
PV = Present Value (the amount of money needed in the savings account at retirement)
PMT = Payment per period (the annual income the man wants to draw, which is $50,000 in this case)
r = Interest rate per period (the Annual Percentage Rate (APR) divided by 100 in this case, which is 5% / 100 = 0.05)
Using this formula, we can calculate the present value (PV) as follows:
PV = $50,000 / 0.05
PV = $1,000,000
Therefore, the man needs to have $1,000,000 in his savings account when he retires in order to be able to draw $50,000 per year indefinitely, assuming a constant annual interest rate of 5%.