Looking at this from a lender perspective........why doesn't the rate used in the loan amortization process (rate used in the PVIFA, (1-(1+i)^-n)/i (assuming annual ordinary annuity), which discounts annuity payments to the PV of initial principal, equal the same rate computed when using CAGR (The principal is PV amount, total payments the FV amount, and the term the number of years(annual)) ((FV/PV)^(1/n))-1. Since discounting is the inverse of compounding, I would assume they would be equal.

What am I missing?? Any help or insight is appreciated