company has decided to purchase equipment, needing to borrow $$100,000$ from its local bank to make the purchase. The bank gives the company two options: $($a$)60-$month installment note with $4\%$ interest or $($b$)120-$month installment note with $8\%$ interest. Lenders often charge a higher interest rate for longer$-$term loans to compensate for additional risk of lending for a longer time period.