Your bank is offering you an account that will pay $25\%$ interest $($an effective two$-$year rate$)$ in total for

a two$-$year deposit. Determine the equivalent discount rate for the following periods:

a$.$ Six months

b$.$ One year

c$.$ One month

$($Note: Be careful not to round any intermediate steps less than six decimal places.$)$

a$.$ Six months

The equivalent discount rate for a period length of six months is

$\%.($Round to two decimal places.$)$

You are saving for retirement. To live comfortably, you decide you will need to save

$$2,000,000$ by the time you are $65.$ Today is your $33$rd birthday, and you decide,

starting today and continuing on every birthday up to and including your $65$th birthday,

that you will put the same amount into a savings account. If the interest rate is $10\%,$

how much must you set aside each year to make sure that you will have $$2,000,000$ in

the account on your $65$th birthday?

The amount to deposit each year must be $

$($Round to the nearest cent.$)$