Carlos wins the lottery! He has a choice between

Option A: $$18,000,000\mathrm{.}00$ received today.

Option B: $23$ payments of $$1,622,862\mathrm{.}74$ at the start of every year for $23$ years, with the first payment today.

The nominal annual interest rate is i$(4)=10\mathrm{.}000\%.$ Carlos wants you to advise them which option to choose.

a$)$ Build a spreadsheet $($see the posted example$)$ to compare the present value of the $2$ options. Which would you recommend?

b$)$ Suppose instead you assumed they would never spend any of the money, instead saving it all until the time of the last payment of Option B$.$ Find the future value of both options at this time. Would this calculation change your recommendation?

c$)$ If the interest rate were i$(4)=5\mathrm{.}000\%$ instead, would that change which option you recommend?

d$)$ Obviously there is some interest rate i$(4)$ at which the present value of the two options is the same. Find that value $($accurate to $3$ decimal places, e$.$g$.3\mathrm{.}456\%)$ using either trial and error or goal seek. $($Warning: if you are using trial and error using only $3$ decimal places for the interest rate, the present values you compute might not match exactly!$)$

the spreadsheet should look something like the attached picture.

Please answer all parts.