Suppose you start saving for retirement when you are $45$ years old. You invest $$5,000$ the first

year and increase this amount by $3\%$ each year to match inflation. How much money will you have

saved after $25$ years if the interest rate earned on the retirement account is $9\%$ per year?

$($a$)$ You will have saved $

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

$($b$)$ On the other hand, you will have saved $

if the interest rate was $3\%$ instead of the original

$9\%.$