# nominal rates and effective rates

I would like some help understanding some basic concepts about converting nominal rates into effective rates, and vice-versa. Some of the terms are a little confusing to me.

Some examples I would like help understanding:

1) If I'm given a 7% semi-annual nominal rate, does that mean the annual nominal rate is simply 14%?

2) Continuing with the above, if my annual nominal rate is 14%, is my annual effective rate also 14% if there is no compounding?

3) If I'm given a nominal rate of interest of 8% a year convertible semi-annually, what is the annual effective rate?
Is the answer to this: $(1 + \frac{0.08}{2})^2 = 1.0816$ --> so, effective annual rate is 8.16%?

Why do actuaries use the term "convertible" instead of "compounded"?

• Because interest, principal could be converted into cash every (say) $6$ months, but not before. So it described a *process, and was not just shorthand for a number. – André Nicolas Feb 22 '14 at 18:12
• @André Nicolas, thank you, that makes sense. But that process still uses the underlying assumption that the cash you receive is reinvested at that interest rate, which is the same principle as compounding. – mrp2181 Feb 22 '14 at 20:08
• I am explaining the origin of the terminology. Effectively, it is compound interest. – André Nicolas Feb 22 '14 at 20:36

1) If I'm given a 7% semi-annual nominal rate, does that mean the annual nominal rate is simply 14%?

No. 7% semi-annual is 3.5% every six months. So annual rate is $1.035^2 - 1$.

2) Continuing with the above, if my annual nominal rate is 14%, is my annual effective rate also 14% if there is no compounding?

Yes it's 14%.

3) If I'm given a nominal rate of interest of 8% a year convertible semi-annually, what is the annual effective rate? Is the answer to this: $(1 + .08/2)^2 = 1.0816$ --> so, effective annual rate is 8.16%?

Yes.

Why do actuaries use the term "convertible" instead of "compounded"?

Beats me.

• Thanks for the quick reply, but a quick follow up question: 1) wouldn't 1.035^2 be the annual effective rate, not the annual nominal rate? – mrp2181 Feb 22 '14 at 18:53
• @user130743 Yes, you are right. I misread it as "7% convertible semi-annually" which is equivalent to 3.5% each six months i.e. 1.035^2-1 per year. But if "7% semi-annual" means "7% each six months" then the annual nominal rate would be "14% convertible semi-annually" and the annual effective rate would be 1.07^2 - 1. – oks Feb 22 '14 at 19:28
• I'm sorry for the confusion. The material I'm looking at isn't very clear as to what term structure the nominal interest rates are given (ie, it doesn't state whether 7% nominal semi-annual rate is in terms of 6 months or 1 year). I'm beginning to think it's in terms of 1 year though. Interest rates aren't new to me, this material, I think, is just terribly worded. Thanks for all your help. – mrp2181 Feb 22 '14 at 19:59