Assume that your credit card statement date is the first day of month. The applied monthly rate is $1\mathrm{.}875\%.$ Your bank capitalizes unpaid interest at the end of each month.

On Jan $1,2024,$ your credit card has an unpaid balance of $$1000.$ Answer the following two questions.

$1)$ What will your credit card balance be after $5$ months, if no other transactions are made during the $5$ months?

a$.$

$1106\mathrm{.}32$

b$.$

$1093\mathrm{.}75$

c$.$

$1097\mathrm{.}33$

d$.$

$1085\mathrm{.}622$If you pay a bill of $$300$ with your credit card on Jan $12,$ what would your credit card balance be in your next month's statement $($Feb $1,2024),$ assuming your bank charges interests starting from the next day of the transaction?

a$.$

$1352\mathrm{.}75$

b$.$

$1305\mathrm{.}98$

c$.$

$1322\mathrm{.}38$

d$.$

$1018\mathrm{.}75$