Suppose you start saving for retirement when you are $40$ 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 $7\%$ 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 $7\%.$