We are considering the effects of starting early or late to save for retirement. Assume that each account considered has an APR of $6\%$ compounded monthly.

Following expert advice, you begin your retirement program as soon as you graduate from college at age $30.$ You plan to retire at the age of $65.$ What monthly contributions do you need to make to

have a retirement account worth $$950,000?($Round your answer to the nearest cent.$)$

$

What will your total personal contribution be by the time you retire if you start saving after graduation?

$

Against expert advice, you begin your retirement program at age $48.$ You plan to retire at the age of $65.$ What monthly contributions do you need to make to have a retirement account worth

$$950,000?($Round your answer to the nearest cent.$)$

$

What will your total personal contribution be by the time you retire if you start saving at age $48?$

$

How much more will you personally contribute by the time you retire if you start saving at age $48$ instead of starting right after graduation?

$