This problem is a complex financial problem that requires several skills, perhaps some from previous sections.

During four years of college, Nolan Ryan's student loans are $$4,000,$$$3,500,$$$4,400,$ and $$5,000$ for freshman year

through senior year, respectively. Each loan amount gathers interest of $1\%,$ compounded quarterly, while Nolan is in school

and $4\%,$ compounded quarterly, during a $6-$month grace period after graduation.

$($a$)$ Assuming the freshman year loan earns $1\%$ interest for $\frac{3}{4}$ year during the first year, then for $3$ full years until

graduation, and making similar assumptions for the loans for the other years, complete the table. $($Round your

answers to the nearest cent. Store the whole value in your calculator.$)$

$($b$)$ What is the loan balance $($in dollars$)$ at the end of Nolan's senior year? $($Round your answer to the nearest

cent.$)$

$

$($c$)$ What is the loan balance $($in dollars$)$ after the grace period? $($Round your answer to the nearest cent.$)$

$($d$)$ After the grace period, the loan is amortized over the next $10$ years at $4\%,$ compounded quarterly. Find the

quarterly payment $($in dollars$).($Round your answer to the nearest cent.$)$

$

$($e$)$ If Nolan decides to pay an additional $$90$ per payment, find the quarterly payment with the additional $$90$

added to each one. $($Round your answer to the nearest cent.$)$

$

$($f$)$ If Nolan does indeed decide to pay an additional $$90$ per payment, how many payments will amortize the debt?

$($Round your answer to two decimal places.$)$

payments

$($g$)$ What amount $($in dollars$)$ should be added to the last payment to pay the loan in full? $($Round your answer to

the nearest cent.$)$

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$($d$)$ How much will Nolan save $($in dollars$)$ by paying the extra $$90$ with each payment? $($Round your answer to the

nearest cent.$)$

$