Rufaro has been a full$-$time student at the University of Manitoba for the past four years. She has just completed her bachelor of commerce degree from the Asper School of Business and her last day of exams was April $20.$ Her total student loan is $$34,000.00.$ She has decided to take her six$-$month grace period and convert it to principal, then start making payments of $$600\mathrm{.}00$ per month using the variable interest rate of prime $+2\mathrm{.}5\%.$ The prime rate at the start of the grace period was $3\mathrm{.}75\%,$ after which it increased by $0\mathrm{.}5\%$ on August $24.$

Complete the table below to determine the total principal Rufaro will owe at the end of the grace period.

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

$\backslash$table$[[$Date Range,$\backslash$table$[[$Balance$],[($P$)]],\backslash$table$[[$Annual$],[$Interest Rate$],[(r)$