Question

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

Answer 1

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

Step-by-step 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.