LO$\mathrm{.}5,8$ Otis is the CEO of Rectify, Inc., a private foundation. Otis invests $$500,000(80\%)$ of the foundation's investment portfolio in high$-$risk derivatives. Previously, the $$500,000$ had been invested in corporate bonds with an AA rating that earned $4\%$ per annum. If the derivatives investment works as Otis's investment adviser claims, the annual earnings could be as high as $20\%.$

a$.$ Determine whether Rectify is subject to any of the taxes imposed on private foundations.

b$.$ If so$,$ calculate the amount of the initial tax.

c$.$ If so$,$ calculate the amount of the additional tax if the act causing the imposition of the tax is not addressed within the correction period.

d$.$ Are Otis and the foundation better off financially if the prohibited transaction, if any, is addressed within the correction period? Explain.