.NET Reflection set private property

If you have a property defined like this:

private DateTime modifiedOn;
public DateTime ModifiedOn
{
    get { return modifiedOn; }
}

How do you set it to a certain value with Reflection?

I've tried both:

dto.GetType().GetProperty("ModifiedOn").SetValue(dto, modifiedOn, null);

and

dto.GetType().GetProperty("modifiedOn").SetValue(dto, modifiedOn, null);

but without any success. Sorry if this is a stupid question but it's the first time I'm using Reflection with C#.NET.