Kristine has $$5,000$ in an account today that pays $3\%$ interest rate. Two years from now she withdraws $$1,000$ from that account to buy a laptop. How much will she have in this account in $6$ years if she does not make any other deposits or withdrawals? Assume annual compounding.

a$.$ $$4,844\mathrm{.}75$

b$.$ $$7,095\mathrm{.}77$

c$.$ $$4,776\mathrm{.}21$

d$.$ $$7,164\mathrm{.}31$

e$.$ $$4,970\mathrm{.}26$

Your grandaunt wants to buy an $($ordinary$)$ annuity that will pay her cost of living of $$70,000$ per year for $20$ years. If the quoted interest rate today is $5\%$ and the annuity compounds monthly, how much does this annuity cost?

a$.$ $$872,354\mathrm{.}72$

b$.$ $$865,404\mathrm{.}52$

c$.$ $$883,897\mathrm{.}66$

d$.$ $$863,824\mathrm{.}15$