Suppose that today $($January $1)$ you deposited $$1,000$ into a savings account that pays $8$ percent.

a$.$ If the bank compounds interest annually, how much will you have in your account three

years from today?

b$.$ What would your balance be in three years if the bank used quarterly compounding

rather than annual compounding?

c$.$ Suppose you deposited the $$1,000$ in four payments of $$250$ each on January $1$ of the

next four years, beginning one year from today. How much would you have in your

account in four years when the last deposit is made assuming that interest is $8$ percent

compounded annually?