You are an actuary for an insurance company that offers a guaranteed minimum withdrawal benefit (GMWB) to its policyholders. The GMWB guarantees a policyholder a minimum annual withdrawal of $20,000 from their retirement savings account until the account balance is depleted. The company has sold 10,000 policies with a total account value of $200 million. The company uses the following assumptions in its GMWB valuation:

• The annual interest rate on the account balance is 5%.
• The policyholders have a life expectancy of 25 years and follow a uniform distribution of death probabilities over the year.
• The annual expense ratio of the GMWB is 1%.

Calculate the amount of reserve that the company needs to set aside to cover the potential payouts of the GMWB policyholders.

(20 marks)