Suppose you borrow $$50,000$ at an annual interest rate of $6\%,$ 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.

$($Use the interactive figure to find your answer.$)$

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

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

$($b$)$ Compared to the $5-$year loan, the total payments for the $10-$year loan will be $ greater. $($Round to the nearest cent as needed.$)$