1. **State the problem:** You have an annuity with a present value (PV) of 50000, and you want to find the payment amount (PMT) for withdrawals every 2 months over 5 years. The interest rate is 5.5% annually, compounded every 2 months. 2. **Identify the formula:** The present value of an annuity formula is: $$PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}$$ where: - $PV$ is the present value, - $PMT$ is the payment per period, - $i$ is the interest rate per period, - $n$ is the total number of payments. 3. **Calculate the values:** - Annual interest rate = 5.5% = 0.055 - Compounded every 2 months means 6 periods per year. - Interest rate per period $i = \frac{0.055}{6} = 0.0091667$ - Number of payments $n = 5 \text{ years} \times 6 = 30$ 4. **Rearrange the formula to solve for $PMT$:** $$PMT = PV \times \frac{i}{1 - (1 + i)^{-n}}$$ 5. **Substitute the values:** $$PMT = 50000 \times \frac{0.0091667}{1 - (1 + 0.0091667)^{-30}}$$ 6. **Calculate the denominator:** $$1 + 0.0091667 = 1.0091667$$ $$1.0091667^{-30} = \frac{1}{1.0091667^{30}}$$ Calculate $1.0091667^{30}$: $$1.0091667^{30} \approx 1.3196$$ So, $$1.0091667^{-30} \approx \frac{1}{1.3196} = 0.7579$$ 7. **Calculate the denominator:** $$1 - 0.7579 = 0.2421$$ 8. **Calculate the payment:** $$PMT = 50000 \times \frac{0.0091667}{0.2421} = 50000 \times 0.03787 = 1893.50$$ **Final answer:** The payment amount is **1893.50** per withdrawal every 2 months for 5 years.