You are the accounting manager for Kool Ragz, Inc., a manufacturer of men's and women's clothing. The company needs to borrow $$1,900,000$ for $90$ days in order to purchase a large quantity of material at "closeout" prices. The interest rate for such loans at your bank, Rimrock Bank, is $15\%$ using ordinary interest.

$($a$)$

What is the amount $($in $$)$ of interest on this loan?

$

$($b$)$

After making a few "shopping" calls, you find that Southside National Bank will lend at $15\%$ using exact interest. What is the amount $($in $$)$ of interest on this offer? $($Round your answer to two decimal places.$)$

$

$($c$)$

So that it can keep your business, Rimrock Bank has offered a loan at $14\mathrm{.}5\%$ using ordinary interest. What is the amount $($in $$)$ of interest on this offer?

$

$($d$)$

$($Challenge$)$ If Southside National wants to compete with Rimrock's last offer $($part c$)$ by charging $$1,875$ less interest, what rate $($as a $\%),$ rounded to the nearest hundredths of a percent, must it quote using exact interest?

$\%$