$4.$ Erin currently has $44,000$ in an account. She will deposit $10,000$ every other year beginning next year and ending nine years from today. She will have $\_\_\_\_\_$ in her account $10$ years from today. Assume the account pays $5\%$ per annum.

a$.132,836\mathrm{.}93$

b$.134,516\mathrm{.}04$

c$.135,004\mathrm{.}15$

d$.136,094\mathrm{.}72$

e$.138,904\mathrm{.}83$

$5.$ You are offered a fixed annual payment of $275$ starting one year from today and continuing yearly until forever. If the discount rate is $7\%$ p$.$a$.,$ then the value today of these cash flows is $\_\_\_\_\_\_\_\_.$

a$.3,671\mathrm{.}43$

b$.3,756\mathrm{.}43$

c$.3,885\mathrm{.}71$

d$.3,928\mathrm{.}57$

e$.4,071\mathrm{.}43$

$6.$ You have invested your money into a project that will pay you $1,000$ starting $5$ years from today $($t $=5)$ and will continue to pay out until $20$ years from today $($t $=20).$ If the interest rate is $6\%$ p$.$a$.,$ then the value of your investment today $($t$=0)$ is $\_\_\_\_\_\_.$

a$.7,206\mathrm{.}80$

b$.7,516\mathrm{.}26$

c$.8,004\mathrm{.}82$

d$.8,493\mathrm{.}01$

Please show the all steps and formulas. Thank you so much!