In fact you re looking for the geometric mean, NOT the arithmetic mean that is suggested in the previous answers. In general, the geometric mean of n. show more In fact you re looking for the geometric mean, NOT the arithmetic mean that is suggested in the previous answers.
In general, the geometric mean of n numbers is the n-th root of their product. In your example with three interest rates of 12, 9, and 16, the average interest rate is (12*9*16)^(1/3) = 12. (Note that we take the cubic root because there are 3 numbers. Note also that the geometric mean is less than the arithmetic mean, which is (12+9+16)/3 = 12.33 and is not appropriate here.)
Here s how you would interpret the geometric mean: If you have three credit cards with EQUAL balances that each have interest rates 12, 9, and 16 percent, then this is exactly equivalent to having the total balance on
one credit with an interest rate of 12 percent. This is the UNWEIGHTED geometric mean because all the balances are the same.
For the WEIGHTED geometric mean, the weights enter EXPONENTIALLY (as opposed to multiplicatively, as in the arithmetic mean). In your case of three cards with three different balances of 7,000, 1,300, and 3,000, the weighted geometric mean is
( 12^7,000 * 9^1,300 * 16^10,000 ) ^ (1/18,300) = 13.76
The weighted mean just takes the weighted n-th root, where n is now just the sum of the weights (which is 18,300). This can be interpreted in the following way: If you have 3 cards with balances 7,000, 1,300, and 10,000 and interest rates 12, 9 and 16, then this is exactly equivalent to having one credit card with the total balance (18,300) at 13.76 percent.
Now it s time to pay down those cards. Best of luck!
dave · 8 months ago