A $40-$year annuity due has annual payments of $6000.$ Assume a nominal interest rate of $8\%$ compounded annually.

a$)$ Determine the accumulated value of the annuity.

b$)$ Assuming a $3\%$ annual effective inflation rate, determine the accumulated value of the annuity using the real rate of return.

c$)$ Determine the present value of the annuity by discounting the accumulated value in part $($a$)$ for $40$ years using the inflation rate in part $($b$)$