How much do you have to deposit today so that beginning $15$ years from now you can withdraw $$13,000$ a year for the next $6$ years $($periods $15$ through $20)$ plus an additional amount of

$$26,000$ in that last year $($period $20)?$ Assume an interest rate of $16$ percent. Answer sub$-$parts $($a$)-($d$)$ below; these break the problem down into smaller parts.

a$.$ What is the value of the $$13,000$ withdrawals in years $15$ through $20$ at the end of year $14$ if the annual interest rate is $16$ percent?

$($Round to the nearest cent.$)$

b$.$ What is the present value today of the $6-$year $$13,000$ annuity at the end of year $14($found in part a$)$ if the annual interest rate is $16$ percent?

$($Round to the nearest cent.$)$

c$.$ What is the present value of the amount of $$26,000$ withdrawal in year $20$ if the annual discount rate is $16$ percent?

$($Round to the nearest cent.$)$

d$.$ How much do you have to deposit today so that beginning $15$ years from now you can withdraw $$13,000$ a year for the next $6$ years $($periods $15$ through $20)$ plus an additional amount of

$$26,000$ in that last year $($period $20)?$

$

$($Round to the nearest cent.$)$