John invests a total of $10,000.$ He purchases an annuity with payments of $1,000$ at the beginning of each year for $10$ years at an effective annual interest rate of $7\%.$ As annuity payments are received, they are reinvested at an effective annual interest rate of $3\mathrm{.}6\%.$ The balance of the $10,000$ is invested in a $10-$year certificate of deposit with a nominal annual interest rate of $7\mathrm{.}9\%,$ compounded quarterly. Calculate the annual effective yield rate on the entire $10,000$ investment over the $10-$year