Gabriela is planning for her retirement. At age $30,$ she received an inheritance of $$50,000,$ which she plans to save for retirement. She also assumes that between age $30$ and $67$ she will invest $$10,000$ per year into an IRA. She wants to determine how much she will have in the bank when she retires at age $67,$ assuming that she receives a $5\%$ annual return on these investments, compounded annually.

a$.$ Use the compound growth formula to calculate the value of Gabriela's inheritance when she attains the age of $67.($Please round to the dollar, e$.$g$.,$ $$450,000,$ not $$450,000\mathrm{.}25)$

b$.$ Use the FV formula to calculate the value of Gabriela's IRA at the time that she retires at age $67.($Please round to the dollar.$)$

c$.$ Gabriela wants to know how much she will get each month if she converts all of her retirement savings to an annuity when she retires. If at age $67,$ Gabriela converts her savings $($from both the inheritance and her annual savings$)$ to a $25-$year annuity, how much income will she receive each year? Assume that the interest rate remains $5\%$ compounded annually and that she has no funds left at the end of the period. $($Please round to the dollar.$)$