Problem $1(24$ points, $8$ points each$)$

Convert

$($a$)4\%$ compounded quarterly to the nominal rate compounded monthly.

$($b$)6\%$ compounded semi$-$annually to the nominal rate compounded contin$-$

uously.

$($c$)$ You have borrowed $$500,000$ from a bank and will pay back this loan

over $30$ years in equal monthly payments. The nominal interest is $8\mathrm{.}5\%$ per

year. How much do you owe the bank immediately after the $60$th monthly

payment?