Jim wants to retire in $30$ years when he turns $60$ years old. He is in good health and expects to live to be $90$ years old. He wants his monthly income to have the same purchasing power as $$15,000$ today on the day he retires and every day thereafter. This could be a challenge because he expects the inflation rate to be $4\%$ per year on average for the rest of his life. Once in retirement, Jim will have to lower the risk of his portfolio because he cannot take the risk suffering significant investment losses. He estimates his lower risk retirement portfolio will produce $8\%$ per year and his income tax rate will be $25\%.$

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Assume that during Jim's saving years, he is able to earn $10\%$ before tax. He expects to still face an income tax rate of $25\%.$ Further, Jim just won the lottery and has a bundle of cash on hand.

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What is the minimum amount Jim would have to put aside today to achieve his goal? $($round to the nearest $$10,000)$

$$1,460,000$

$$1,260,000$

$$5,400,000$

$$940,000$