Mitch and Bill are both age $75.$ When Mitch was $25$ years$$ old, he began depositing $$$$1000$ per year into a savings account. He made deposits for the first $10$ years, at which point he was forced to stop making deposits.$$ However, he left his money in the$$ account, where it continued to earn interest for the next $40$ years. Bill$$ didn't start saving until he was $45$ years$$ old, but for the next $30$ years he made annual deposits of $$$$1000.$ Assume that both accounts earned an average annual return of $7\%($compounded once a$$ year$).$a$.$ How much money does Mitch have in his account at age$75?$

At age$75,$ Mitch has $$$

$$

enter your response here in his account.

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

Part $2$

b$.$ How much money does Bill have in his account at age$75?$

At age$75,$ Bill has $$$

$$

enter your response here in his account.

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

Part $3$

c$.$ Compare the amounts of money that Mitch and Bill deposit into their accounts.

Mitch deposits $$$

$$

enter your response here in his account and Bill deposits $$$

$$

enter your response here in his account.

Part $4$

d$.$ Draw a conclusion about this parable. Choose the correct answer below.

A$.$

Bill ends up with more money in his account than Mitch because he make more deposits than$$ Mitch, and each additional deposit will accrue interest each year.

B$.$

Both Bill and Mitch have the same return on their investments despite using different methods of saving.

C$.$

Mitch ends up with more money in his account despite not having deposited as much money as Bill because the interest that is initially accumulated accrues interest throughout the life of the account.

D$.$

Both Bill and Mitch end with the same amount of money in their$$ accounts, but Mitch had to deposit less money using his method. It is better to start saving as early as possible.