A previously issued $A2,15-$year industrial bond provides a return $25\%$ higher than the prime interest rate of $11$ percent. Previously issued A$2$ public utility bonds provide a yield of three$-$eighths of a percentage point higher than previously issued A$2$ industrial bonds of equal quality. Finally, new issues of $A2$ public utility bonds pay one$-$fourth of a percentage point more than previously issued $A2$ public utility bonds.

What should be the interest rate on a newly issued A$2$ public utility bond?

Note: Do not round intermediate calculations. Input your answer as a percent rounded to $3$ decimal places.

Interest rate $6$