In order to make a solid and successful financial plan, we need to know what we want at different time horizons. One of the most important, and longest horizon, goals is saving for retirement. Kathy and John both plan to work another $35$ years and retire at $65$ years old. Kathy$$s $401$k is a Lifecycle plan, which means that it shifts towards lower$-$risk assets as she approaches $65$ years old. It is expected to earn $10\%$ until she is $50$ years old, when it will shift to earn $8\%$ until she is $60$ years old. It will then shift again to return $5\%$ until she is $65$ years old and will retire.

Kathy and John do not want to worry about running out of money, so they plan to live until they are $100$ years old $(35$ years of retirement$).$ They want to be able to withdraw today$$s value $(2024)$ of $$8,333$ a month for an annual income of $$100,000$ a year during retirement. They also understand inflation, and they want $$100,000$ worth in today$$s dollars. They recognize they need to save more for retirement, so they plan to open a Roth IRA and maximize it by making monthly contributions of $$541\mathrm{.}67($the annual maximum amount is $$6,500$ per account$).$ They decide to go into a fund that expects to earn $11\%$ and they plan to move that into a lower risk $6\%$ plan when they turn $50$ years old. When they retire they will move the $401$k savings into a low$-$risk fund that earns $3\mathrm{.}5\%$ and the Roth IRA savings into a safe bond$-$fund that earns $3\%.$ If they are still short on their goals, they will open a second Roth IRA and contribute only enough to meet their goals. The fund they would choose for this would be expected to earn $12\%$ and they would shift this at age $55$ into a fund earning $5\%$ for safety and not make any more contributions. At retirement, it would be shifted into a bond$-$fund that would return $3\%.$

Consider how much will be in Kathy$$s $401$k when she retires at $65.$ Note that the employer also contributes some to her retirement. The fund shifts returns, so multiple steps will be required. Then determine what her monthly withdrawal will be from this account.