Final answer:
An uncle with $3,065,359 saved for retirement needs to calculate a fixed annual withdrawal at a 9% annual rate over 30 years to deplete his savings. The annuity formula P = (r × PV) / [1 - (1 + r)^(-n)] is used to determine the fixed payments. Substituting the given values into the formula, we calculate the precise amount to withdraw each year.
Step-by-step explanation:
The student's question involves determining how much an uncle, who is 75 years old with $3,065,359 saved for retirement, should withdraw annually at a 9% annual rate over the next 30 years to deplete his savings entirely. To solve this, we use the annuity formula, which calculates the fixed payments over a certain period at a specified interest rate. The formula is: P = (r × PV) / [1 - (1 + r)^(-n)], where P is the payment, r is the annual interest rate, PV is the present value, and n is the number of payments.
Calculating the Annual Withdrawal
To find out the exact withdrawal amount, we need to plug the values into the formula:
PV (Present Value of Retirement Savings) = $3,065,359
r (Annual Interest Rate as a decimal) = 0.09
n (Number of Years) = 30
The formula for the yearly withdrawal then becomes:
P = (0.09 × 3,065,359) / [1 - (1 + 0.09)^(-30)], calculating this gives us the fixed annual amount the uncle needs to withdraw to use all his savings by the end of the 30 years.