[Math] nominal rates and effective rates

actuarial-sciencefinance

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"?

Thanks in advance.

Best Answer

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.

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