Suppose a rancher wants to borrow $$163,835\mathrm{.}00$ to buy a tract of land. The BCS bank will make a $26-$year loan fully amortized at $10\mathrm{.}84\%($annual payments$).$ A $$476\mathrm{.}00$ loan fee and stock purchase is required. The borrower stock requirement is the lesser of $$1,000$ or $4\mathrm{.}00\%$ of loan amount.

$($i$)$ Calculate the loan principal.

a$.$ $$171,157\mathrm{.}29$

b$.$ $$165,337\mathrm{.}10$

c$.$ $$165,311\mathrm{.}00$

d$.$ $$170,791\mathrm{.}04$

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$($ii$)$ Calculate the required stock purchase.

a$.$ $$6,598\mathrm{.}10$

b$.$ $$1,596\mathrm{.}76$

c$.$ $$6,612\mathrm{.}44$

d$.$ $$1,000\mathrm{.}00$

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$($iii$)$ Calculate the annual loan payments.

a$.$ $$19,244\mathrm{.}67$

b$.$ $$19,932\mathrm{.}45$

c$.$ $$19,254\mathrm{.}65$

d$.$ $$19,889\mathrm{.}80$

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$($iv$)$ Calculate the APR.

a$.2\mathrm{.}74\%$

b$.10\mathrm{.}84\%$

c$.10\mathrm{.}96\%$

d$.,10\mathrm{.}50\%$

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