How are CAGR and compounding frequency related?

Question

I am newbie, so forgive me if my question seems trivial. I have a numerical where a bank scheme triples a person's investment in 5 years but it doesn't talk about the compounding frequency. Assuming it to be compounding yearly I get a CAGR of 24.57%.

I was wondering does the compounding period matter? Will I end up getting the effective yield per year as 24.57 % even for semi annual, quarterly or monthly compounding periods? I know there is a difference between nominal rate and effective rate. Is CAGR the effective rate which would stay the same irrespective of compounding period which would only change the nominal rate??

Answer 1

In your context, no, the compounding frequency does not matter. You are calculating the effective annual rate for a 200% return over 5 years, which would be:

   (1+r)^5 = 3
==>    1+r = 3 ^ 1/5
==>    1+r = 1.2457
==>      r = 24.57%

Where the compounding frequency will matter is when you calculate the nominal rate, meaning how much the investment grows in each period. For example, the monthly rate (annualized) would be:

 1.2457 ^ (1/12) - 1 = 1.847% (22.17% annualized)

For daily compounding it would be:

1.2457 ^ (1/365) - 1 = 0.06% (21.98% annualized)