$(5-$Button Solution;$$You can refer to$$Example $6-13)$

Tang has a $4\%$ mortgage with monthly payments for $30$ years. Her original balance was $$250,000,$ and she just made her twenty$-$fourth payment.

$($a$)$ Her monthly payment is $Question Blank $1$ of $4.$

$($Rounding answers to$$the nearest dollars$)$

$$

$($b$)$ After the $24$th payment, now the remaining balance is $Question Blank $2$ of $4.$

$($Rounding answers to$$the nearest dollars$)$

$$

$($c$)[($b$)$ continued$]$

Tang received a bonus last month, so she decides to pay an extra $$3,000$ in loan now. Then she can shorten the loan for Question Blank $3$ of $4$ months.

$($Rounding answer to$$the nearest whole number$)$

$$

$($d$)[($b$)$ continued$]$

If Tang increases each loan payment to $120\%$ of her current loan payment, she can shorten the loan by Question Blank $4$ of $4$ months.

$($Rounding answer to$$the nearest whole number$)$