Pascale has just finished college and started her career. She plans to start saving money early so that she can retire at age $55.$ She decides that she needs $$800000\mathrm{.}00$ when she retires.

a$)$ How much does Pascal need to deposit monthly into an investment that earns $8\%/$a$,$ compounded monthly if she starts when she is $25$ years old?

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b$)$ What would her required monthly payments be if she didn$$t start saving until age $40?$

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