Rajesh and Priya plan to retire at age $60$ with a retirement income of $$48,000$ a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that withdrawing payments of $$12,000$ at the beginning of each quarter of gives them the right balance of liquidity and maximized interest earnings. They feel they can safely earn an interest rate of $5\mathrm{.}75\%,$ compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are $90$ years old.

How much money will they have to have saved by the time they are $60$ and ready to begin their retirement, in order fulfill this plan? $[$Blank$-1]$

If the same total calculated above was to be saved, but no interest earned whatsoever, how much would be available to live on each quarter? $[$Blank$-2]$

If the full $30$ years are lived and quarterly budget spent, how much money in total will have been utilized in retirement? $[$Blank$-3]$

How much will have been earned in interest? $[$Blank$-4]$

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Now that Rajesh and Priya have their saving goal calculated, and rounded up to the nearest dollar, they want to start budgeting to reach that goal. They are $40$ years old currently, so they have just $20$ years to save up the total nest egg retirement amount they calculated. If they assume the same interest rate, and compound frequency, but make deposits into their savings at the beginning of every month, how much would their deposit have to be each month to satisfy their retirement nest egg goal on time?

If they assume the same interest rate and compound frequency, but make deposits into their savings at the beginning of every month, how much would their deposit have to be each month to satisfy their retirement nest egg goal on time?$[$Blank$-1]$

How much interest will be earned? $[$Blank$-2]$

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