Consider a person who begins contributing to a retirement plan at age $25$ and contributes for $40$ years until retirement at age $65.$ For the first $10$ years, she contributes $$262$ per month. She increases the contribution rate to $$428\mathrm{.}67$ per month in years $11$ through $20.$ This is followed by increases to $$845\mathrm{.}33$ per month in years $21$ through $30$ and to $$1,262$ per month for the last $10$ years. This money earns a $8$ percent return.

First compute the value of the retirement plan when she turns age $65.$

Compute the monthly payment she would receive over the next $40$ years if the wealth was converted to an annuity payment at $5$ percent.