Please solve the following time value of money problems. $(12$ points total$)$

a$.$ If you deposit $$1800$ in an account that pays $3\mathrm{.}75\%$ interest annually, how much will you have after $6$ years?

b$.$ What is the present value of a security that will pay $$42,000$ in $13$ years if securities of equal risk pay $5\mathrm{.}25\%$ annually?

c$.$ You have $$81,455\mathrm{.}75$ in a brokerage account, and you plan to deposit an additional $$22,000$ at the end of each future year until your account reaches $$500,000.$ You expect to earn $9\%$ annually on the account. How long will it take to reach your goal?

d$.$ You just received an inheritance worth $$200,000.$ You want to retire in $25$ years and you don't plan to make any additional contributions. If you need $$1,000,000$ in order to retire, what interest rate must you earn in order to reach your goal?

e$.$ An investment will pay $$300$ at the end of each of the next $3$ years, $$150$ at the end of Year $4,$ $$500$ at the end of Year $5,$ $$700$ at the end of Year $6,$ and $$400$ at the end of Year $7.$ If other investments of equal risk earn $6\mathrm{.}75\%$ annually, what is the present value of the cash flow stream?

f$.$ Using the same information from part e$,$ what is the future value of the cash flow stream?