You make a one time investment in the following way: you purchase a $50$ year bond with semiannual coupons, face value of $$12,000,$ a coupon rate of $r^{(2)}=4\%$ and a yield rate of $i^{(2)}=6\%.$ Immediately after receiving each coupon you reinvest the coupon into an account earning an interest rate of $i^{(2)}.$ If the total from this investment after $50$ years $($AV of coupons $+$ redemption$)$ is $$160,000$ then find $i^{(2)}$ and find the equivalent effective annual interest rate over the $50$ year period.