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You just graduated and you have a job. You want to save using a Roth IRA since any growth is tax exempt. You are concerned

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You just graduated and you have a job. You want to save using a Roth IRA since any growth is tax exempt. You are concerned about inflation, which you estimate will be 1.5% per year. The contribution limit is $6000 per year in 2020, so you plan on depositing $500 per month starting in one month until you retire 44 years from now. You estimate your retirement account will grow at about 7% per year while you are saving, but once you retire you will invest in safer assets that will only yield 1.4% per year. Each of these compound monthly. You plan on withdrawing from your Roth IRA each month the same amount each month in retirement as $7000 is worth today (use inflation compounded yearly to figure out the withdrawal amount). How long (in months) will your retirement savings last

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