I think you have your terms confused. The effective rate is the compound annual growth rate (CAGR). It doesn't matter how often the interest is compounded unless you are after the nominal or annual rate BEFORE compounding.
The CAGR formula is:
CAGR = (fv/pv) ^ (1/t) - 1
CAGR = (5750/2000) ^ (1/15) - 1
CAGR = 0.072941038 or about 7.29% rounded to 2 decimals.
FYI, the annual rate (r) would be
r = n * (((fv/pv) ^ (1/t)) ^ (1/n) - 1)
r = 365 * (((5750/2000) ^ (1/15)) ^ (1/365) - 1)
r = 0.070410302 or about 7.04% compounded daily rounded to 2 decimals.
The effective interest rate based on daily compounding is 7.04% and I solved it on a trial and error basis with this online financial calculator:
http://www.moneychimp.com/articles/finwo...
what is the effective rate of interest of an account if it pays interest compounded daily and $2000 grows to $5750 over a 15 year period?
