Suppose you borrow$$ $$50,000$ at an annual interest rate of $5\%,$ with $2$ interest periods a year. You have the option of paying the loan over a$5-$year or$10-$year period. Compare the values of each payment and the total of payments for both loan periods.

$($a$)$ Compared to the $10-$ year loan, each payment of the $5-$ year loan will be $ greater