1. **State the problem:** Farah has 600000 in her RRSP and wants to buy an annuity that pays 3500 monthly with an interest rate of 5% compounded annually. We need to find how long (in months) she will receive payments. 2. **Identify variables:** - Present value (PV) = 600000 - Monthly payment (PMT) = 3500 - Annual interest rate (r) = 5% = 0.05 - Monthly interest rate (i) = \frac{0.05}{12} = 0.0041667 - Number of months (n) = ? 3. **Use the present value of an ordinary annuity formula:** $$PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}$$ 4. **Plug in known values:** $$600000 = 3500 \times \frac{1 - (1 + 0.0041667)^{-n}}{0.0041667}$$ 5. **Isolate the term with n:** $$\frac{600000 \times 0.0041667}{3500} = 1 - (1.0041667)^{-n}$$ Calculate left side: $$\frac{600000 \times 0.0041667}{3500} = \frac{2500}{3500} = 0.7142857$$ So, $$0.7142857 = 1 - (1.0041667)^{-n}$$ 6. **Solve for the exponential term:** $$(1.0041667)^{-n} = 1 - 0.7142857 = 0.2857143$$ 7. **Take natural logarithm of both sides:** $$-n \ln(1.0041667) = \ln(0.2857143)$$ 8. **Calculate logarithms:** $$\ln(1.0041667) \approx 0.004158$$ $$\ln(0.2857143) \approx -1.25276$$ 9. **Solve for n:** $$-n \times 0.004158 = -1.25276$$ $$n = \frac{1.25276}{0.004158} \approx 301.3$$ 10. **Round to nearest month:** $$n \approx 301 \text{ months}$$ **Final answer:** Farah will receive payments for approximately **301 months**.