# Average interest rate vs compound interest rate (1) Taking an average of %profit

(2) Is calculating %profit by (end-start/start)*100

(3) Is (2) divided by 10 periods

My questions are;

1. What is the REASON why (1) and (3) are different values?

2. What would the compound interest figure be for periods 1 through to 10?

• Is this a homework? – littleadv Aug 1 '14 at 7:29
• Not homework. Just a curiosity! – user19388 Aug 1 '14 at 7:58
• (1) and (3) are not equal because of the laws of arithmetic. In general, a/b + c/d does not equal (a+c)/(b+d). – Dilip Sarwate Aug 1 '14 at 8:56

I'll give you one simple example -

• year 1 +10%
• year 2 -10%

The average is 0% return, breakeven, right? But 1.1 * .9 = .99. If \$100 gains 10% you end year one with \$110, but lose 10% and you have \$99.

(2) is the cumulative rate of return. It is the final period's end of period value divided by the initial period's start of period value:

``````100% ( final / initial - 1 )
``````

(3) is the arithmetic mean of the total return, which is very non-standard:

``````cumulative rate of return / number of time periods
``````

(1) is the arithmetic mean of the period profit percentages which is a simple average:

``````SUM( periodic profit percentage ) / number of periods
``````

NOTE: For such low rates, the geometric and arithmetic means will be almost identical, as discovered by Irving Fisher.