Suppose that you reach 65 years old, and have $100,000 in an investment that pays a return of 5 percent per year. a) If you withdraw $10,000 at the end of each year for living expenses, how many years will it take before your investment is gone

It will take approximately 14.21 years before the investment is gone.

Explanation:

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

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

Where;

PV = Present value or investment value = $100,000

P = Annual withdrawal = $10,000

r = return rate = 5%, or 0.05

n = number of more years it will take before the investment is gone = ?

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

100,000 = 10,000 * ((1 - (1 / (1 + 0.05))^n) / 0.05)

100,000 / 10,000 = (1 - (1 / 1.05)^n) / 0.05

10 = (1 - (1 / 1.05)^n) / 0.05

10 * 0.05 = 1 - (1 / 1.05)^n

0.50 = 1 - (1 / 1.05)^n

(1 / 1.05)^n = 1 - 0.50

0.952380952380952^n = 0.50

Loglinearize both sides, we have:

n * log0.952380952380952 = log0.50

n = log0.50 / log0.952380952380952

n = -0.301029995663981 / -0.0211892990699382

n = 14.2066990828904

Approximating to 2 decimal places, we have:

n = 14.21

Therefore, it will take approximately 14.21 years before the investment is gone.

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