public abstract class InterestRate {

    // irrelevant details

    public static T ImpliedRate<T>(
        double factor,
        double time,
        DayCounter dayCounter
    ) where T : NonCompoundedInterestRate {
        MethodInfo methodInfo = typeof(T).GetMethod(
            "ImpliedRate",
            BindingFlags.Static);
        return (T)methodInfo.Invoke(
            null,
            new object[] { factor, time, dayCounter }
        );
    }

    public static T ImpliedRate<T>(
        double factor,
        double time,
        DayCounter dayCounter,
        Frequency frequency
    ) where T : CompoundedInterestRate {
        MethodInfo methodInfo = typeof(T).GetMethod(
            "ImpliedRate",
            BindingFlags.Static);
        return (T)methodInfo.Invoke(
            null,
            new object[] { factor, time, dayCounter, frequency }
        );
}

public static class InstanceMap
{
    private static readonly Dictionary<Type,object> instances =
        new Dictionary<Type,object>();

    public static void AddInstance(object instance)
    {
        instances[instance.GetType()] = instance;
    }

    public static T GetInstance<T>() { return (T) instances[typeof(T)]; }
}

public interface INonCompoundedInterestRate
{
    INonCompoundedInterestRate ImpliedRate(double factor,
        double time,
        DayCounter dayCounter);
}

public class MyNonCompoundedInterestRate: INonCompoundedInterestRate
{
    public INonCompoundedInterestRate ImpliedRate(double factor,
        double time,
        DayCounter dayCounter) { /* do smth*/ }

    static MyNonCompoundedInterestRate()
    {
        InstanceMap.AddInstance(new MyNonCompoundedInterestRate());
    }
}

public abstract class InterestRate {
    public static T ImpliedRate<T>(
        double factor,
        double time,
        DayCounter dayCounter
    ) where T : INonCompoundedInterestRate
    {
        return InstanceMap.GetInstance<T>().
            ImpliedRate(factor, time, dayCounter);
    }
    // ...
}

public static class InterestRateFactories
{
    static InterestRateFactories()
    {
        _factories = new List<IInterestRateFactory>();
        //  register default factories, although you can also register them elsewhere, like in your ioc setup
    }
    private static readonly List<IInterestRateFactory> _factories;
    public static void RegisterFactory(IInterestRateFactory factory)
    {
        _factories.Add(factory);
    }
    public static T ImpliedRate<T>(double factor, double time, DayCounter dayCounter)
        where T : NonCompoundedInterestRate
    {
        var factory = _factories.FirstOrDefault(x => x.CanCreate(typeof(T), false));
        if (factory == null)
        {
            throw new NotSupportedException("Cannot create a non-compounded implied interest rate of type " + typeof(T).Name);
        }
        return (T)factory.Create(factor, time, dayCounter);
    }
    public static T ImpliedRate<T>(double factor, double time, DayCounter dayCounter, Frequency frequency)
        where T : CompoundedInterestRate
    {
        var factory = _factories.FirstOrDefault(x => x.CanCreate(typeof(T), false));
        if (factory == null)
        {
            throw new NotSupportedException("Cannot create a compounded implied interest rate of type " + typeof(T).Name);
        }
        return (T)factory.Create(factor, time, dayCounter, frequency);
    }
}

public interface IInterestRateFactory
{
    bool CanCreate(Type nonCompoundedInterestRateType, bool compounded);
    NonCompoundedInterestRate Create(double factor, double time, DayCounter dayCounter);
    CompoundInterestRate Create(double factor, double time, DayCounter dayCounter, Frequency frequency);
}