Jeff is retired and has an investment fund worth $210 000 in an RRSP, which earns 9% compounded semi-annually. He plans to withdraw only $2000 at the beginning of each month starting today. When will the fund become depleted?

Question

Quizplus · Accepted Answer

The fund will become depleted in 16 years and 6 months.The formula for the future value of an annuity is:FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)where:P is the present value of the annuityr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:P = $210,000r = 9%n = 2t = 16.5Plugging these values into the formula, we get:FV = $210,000 * ((1 + 0.09/2)^(2*16.5) - 1) / (0.09/2)= $210,000 * 2.335= $490,350This means that the fund will be worth $490,350 after 16.5 years. However, Jeff is planning to withdraw $2,000 at the beginning of each month, which means that he will withdraw $24,000 per year. Therefore, the fund will be depleted in 16.5 years - $210,000/$24,000 = 6 months.

Jeff Is Retired and Has an Investment Fund Worth $210