Eric, age $54,$ funds a Charitable Remainder Annuity Trust $($CRAT$)$ with $$750,000$ in case and securities$.$ In exchange, the trust provides for an annuity $($annual$,$ of course$)$ of $10\%$ of the initial fair market value of the assets. Assume a Section $7520$ rate of $10\%.$ Given these facts, calculate the income interest, the remainder interest, Eric's implicit life expectancy, and the amount Eric can deduct in the year of the transfer as a charitable income tax deduction, subject to AGI limitations as identified in the textbook. Show your math in arriving at your answer.