Use a financial calculator: $(10$ points$)$ An inheritance in the amount of $x$ is divided equally between three siblings Mark, Wayne and Rebecca. Mark uses his share to purchase a five year annuity immediate having equal monthly payments of $Y.$ The price of Mark's annuity is calculated based on a nominal rate of interest of $12\%$ convertible monthly. Wayne uses his share to purchase a perpetuity immediate having annual payments of $5000.$ The price of Wayne's perpetuity is based on an annual effective interest rate of $i.$ Rebecca uses her share to purchase an annuity which pays $100,000$ today, $Y$ in one year and $Y$ in two years.

The price of Rebecca's annuity is based on an annual effective interest rate of $5\%.$ Find $i.$