Your Aunt Ruth has $540,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i. e., run the account down to zero

It will take 28 years for Aunt Ruth to exhaust her funds.

Explanation:

This can be calculated using the formula for calculating the present value (PV) of annuity due given as follows:

PV = P * ((1 - [1 / (1 + r))^n) / r) * (1 + r) (1)

Where;

PV = Present value or amount invested = $540,000

P = Monthly withdraw = $40,000

r = interest rate = 6.5%, or 0.065

n = number of years = ?

Substitute the values into equation (1) and solve for n, we have:

540,000 = 40,000 * ((1 - (1 / (1 + 0.065))^n) / 0.065) * (1 + 0.065)

540,000 / 40,000 = ((1 - (1 / 1.065)^n) / 0.065) * 1.065

13.50 = ((1 - 0.938967136150235^n) / 0.065) * 1.065

13.50 / 1.065 = (1 - 0.938967136150235^n) / 0.065

12.6760563380282 = (1 - 0.938967136150235^n) / 0.065

12.6760563380282 * 0.065 = 1 - 0.938967136150235^n

0.823943661971833 = 1 - 0.938967136150235^n

0.938967136150235^n = 1 - 0.823943661971833

0.938967136150235^n = 0.176056338028167

Log linearizing, we have:

n log0.938967136150235 = log0.176056338028167

n = log0.176056338028167 / log0.938967136150235

n = -0.754348335711024 / -0.0273496077747565

n = 27.5816875299865

Rounding to a whole number, we have:

n = 28

Therefore, it will take 28 years for Aunt Ruth to exhaust her funds.

answer: tell me how

explanation: