$.$ Lauren invests $$10,000$ at a simple interest of $10\%.$ How much interest will Lauren earn after $5$ years? How much total will be in the account after $5$ years?

$4.$ How long would it take $($to the tenth of a year$)$ for $$50,000$ to be $$75,000$ if it is invested at $12\%$ compounded monthly?

$5.$ You are currently $25$ years old, and have started contributing $$300$ at the end of every month towards your retirement account, which earns $5\%$ per year. You will contribute every month, until you retire at $60$ years $(35$ years of contributions$).$ Once you retire, you want to withdraw monthly payments such that at age $90(30$ years of withdrawals$),$ you still have $$100,000$ left in the account. How much will your monthly withdrawals be$?$

$6.$ After shopping for a while for a house, you just found a $$550,000$ house on the market and you have decided to buy it$.$ The bank is asking for a $20\%$ deposit, which you will afford. The bank will finance the loan amount with a $30-$year fixed rate mortgage at $6\mathrm{.}00\%$ interest. Ignore closing costs and all other costs.

a$)$ What will be your monthly payments for this mortgage?

b$)$ If you pay an extra $$250$ per month, how long $($in years$)$ will it take you to pay off the mortgage?

c$)$ If you take the action above, how much interest will you save?