Question

Mr. Deneau accumulated $80,000 in an RRSP. He converted the RRSP into a RRIF and started to withdraw $1400 at the end of every month from the fund. If interest is 10.8% compounded quarterly, for how long can Mr. Deneau make withdrawals? State your answer in years and months (from 0 to 11 months).

Answer 1

Mr. Deneau can make withdrawals for approximately 55 years and 11 months.

Step-by-step explanation:

To find out how long Mr. Deneau can make withdrawals, we need to determine how many monthly withdrawals of $1400 will be possible before the balance in the RRIF is depleted. To do this, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, the principal P is $80,000, the interest rate r is 10.8% (or 0.108), and the interest is compounded quarterly, so n is 4. We want to find the value of t. Let's rearrange the formula to solve for t:

A = P(1 + r/n)^(nt)

80,000 = 80,000(1 + 0.108/4)^(4t)

1 = (1 + 0.108/4)^(4t)

1 = (1 + 0.027)^t

1 = (1.027)^t

Using logarithms, we can solve for t:

t = log1.027(1)

t ≈ 55.96

Since we are dealing with months, we can approximate the time in years and months as 55 years and 11 months. So, Mr. Deneau can make withdrawals for approximately 55 years and 11 months.