27.03.2023 - 17:07

# Mr. Deneau accumulated $100,000 in an RRSP. He converted the RRSP into an RRIF and started to withdraw$4,500 at the end of every three months from the fund. If interest is 6.75% compounded monthly, for how long can Mr. Deneau make withdrawals?

Question:

Mr. Deneau accumulated $100,000 in an RRSP. He converted the RRSP into an RRIF and started to withdraw$4,500 at the end of every three months from the fund. If interest is 6.75% compounded monthly, for how long can Mr. Deneau make withdrawals?

Using the formula for the present value of an annuity due, we can calculate the total number of withdrawals Mr. Deneau can make before his RRIF is depleted. PV = PMT * ((1 - (1 + r)^-n) / r) * (1 + r) Where PV is the present value of the RRIF (which we know is $100,000), PMT is the withdrawal amount ($4,500), r is the monthly interest rate (6.75%/12 = 0.5625%), and n is the total number of withdrawals. Plugging in these values, we get: 100,000 = 4,500 * ((1 - (1 + 0.005625)^-n) / 0.005625) * (1 + 0.005625) Simplifying this equation, we get: 100,000 = 4,500 * ((1 - 0.99439^-n) / 0.005625) * 1.005625 Dividing both sides by 4,500 and multiplying by 0.005625, we get: n = -ln(1 - (100,000 * 0.005625 / 4,500)) / ln(1.005625) Solving this equation, we find that Mr. Deneau can make 69 withdrawals before his RRIF is depleted. To calculate how many years this represents, we divide the total number of withdrawals by the number of withdrawals per year: 69 / 4 = 17.25 Therefore, Mr. Deneau can make withdrawals from his RRIF for \approx imately 17 years and 3 months.
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