Assume the rate of interest is $8\%.$ How much would you need to set aside to provide each of the following?

a$.$ $$1$ billion at the end of each year in perpetuity. $($Enter your answer in billions rounded to $1$ decimal place.$)$

b$.$ A perpetuity that pays $$1$ billion at the end of the first year and that grows at $4\%$ a year. $($Enter your answer in billions rounded to $1$ decimal place.$)$

c$.$ $$1$ billion at the end of each year for $20$ years. $($Do not round intermediate calculations. Enter your answer in billions rounded to $3$ decimal places.$)$

d$.$ $$1$ billion a year spread evenly over $20$ years. $($Do not round intermediate calculations. Enter your answer in billions rounded to $3$ decimal places.$)$

Answer is complete but not entirely correct.

$\backslash$table$[[],[$a$.,$Present value,$$,12\mathrm{.}5,$billion,,$],[$b$.,$Present value,$$,25\mathrm{.}0,$billion,,$],[$c$.,$Present value,$$,9\mathrm{.}818,$billion,,$],[$d$.,$Present value,$$,9\mathrm{.}818ox,$billion,,$]]$