How much do you have to deposit today so that beginning $10$ years from now you can withdraw $ $13$ comma $000$ a year for the next $4$ years$($periods $10$ through $13)$ plus an additional amount of $$$$26$ comma $000$ in that last year$($period $13)?$ Assume an interest rate of $7$ percent. Answer$$ sub$-$parts $($a$)-($d$)$ below; these break the problem down into smaller parts.

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Part $1$

a$.$ What is the value of the $$$$13$ comma $000$ withdrawals in years $10$ through $13$ at the end of year $9$ if the annual interest rate is $7$percent$?$

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

b$.$ What is the present value today of the $4-$year $$$$13$ comma $000$ annuity at the end of year $9($found in part$$ a$)$ if the annual interest rate is $7$percent$?$

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

c$.$ What is the present value of the amount of $$$$26$ comma $000$ withdrawal in year $13$ if the annual discount rate is $7$percent$?$

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

d$.$ How much do you have to deposit today so that beginning $10$ years from now you can withdraw $$$$13$ comma $000$ a year for the next $4$ years$($periods $10$ through $13)$ plus an additional amount of $$$$26$ comma $000$ in that last year$($period $13)?$

$$$

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