Complete the following table, which shows the monthly payments on a $$100,000,30-$year mortgage at the interest rates shown. Use this information to answer the following questions. $($Round your answers to the nearest cent.$)$

$\backslash$table$[[\backslash$table$[[$Amount of$],[$Mortgage $($$$)]],\backslash$table$[[$Interest$],[$Rate $(\%)]],\backslash$table$[[$Monthly$],[$Payment $($$$)]]],[100,000,3,421\mathrm{.}60],[100,000,4,477\mathrm{.}42],[100,000,5,536\mathrm{.}82],[100,000,6,599\mathrm{.}55],[100,000,7,665\mathrm{.}30],[100,000,8,733\mathrm{.}76]]$

$($a$)$ What is the difference in monthly payments between a $$100,000,30-$year mortgage secured at $7\frac{\%}{?}$ year and one secured at $3\frac{\%}{?}$ year?

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$($b$)$ Use the table to calculate the monthly mortgage payments on a $$140,000$ mortgage at $6\frac{\%}{?}$ year over $30$ years. $

Use the table to calculate the monthly mortgage payments on a $$30,000$ mortgage at $6\frac{\%}{?}$ year over $30$ years. $