Lacy has a $$40,500\mathrm{.}00$ student loan when she graduates on May $4,$ and the prime rate is set at $4\mathrm{.}75\%.$ She has decided at the end of the grace period to convert the interest to principal, and she sets her

fixed monthly payment at $$900\mathrm{.}00.$ She opts for the variable rate on her student loan. Create the first four repayments of her repayment schedule. Calculate the total interest charged for both the grace period

and the four payments combined. Assume February does not involve a leap year.

$($Round all monetary values to the nearest penny.$)$

$($Use a minus sign before the dollar sign to denote a negative monetary value. For example, $"-$$$149\mathrm{.}63".)$

$($Give all "Number of Days" quantities as fractions with denominator $365.)$

Total combined interest charged for grace period and first four months:

Note: You can earn partial credit on this problem.