We can use average rate of return which is Return on Investment divided by the principal over time - but we don’t. We almost always use CAGR which looks at your return as annual compounded interest. So obviously for APR (Annual Percentage Rate) We would do the same thing right? It makes sense that if I loan you money my Rate of Return should be your APR. But it’s not. APR is the average meaning costs divided by principal over time.
Why this dichotomy or do I have something wrong?
They are different, but they can equal each other in some circumstances. What you’re missing is reinvestment of the interest.
APR is basically how much the principal grows each year. If you owed $1000, 10% APR is $100. $900 is $90. etc. You get it.
CAGR is the percent that accounts for the total growth over the period, based on some frequency of compounding.
Say in that first year you paid $90 in interest. If you accounted for that interest payment growing over the remaining term of the loan at the same rate as the loan APR such that at the end of the term it was worth $212 (or whatever), then did the same for all the other interest payments, the CAGR you’d compute would equal the APR.
That isn’t always possible in the real world and that’s what they call reinvestment risk.
APR ignores intra-year compounding. So if you take out a $100 one year loan at 12% APR with monthly payments and repayment of principal at the end your interest payments would be $1 each month. The annual rate of return that the lender would earn would not be 12% but (1.01)[sup]12[/sup] -1 = 12.68%.
APR was introduced to protect consumers not against misunderstanding of compounding but to prevent the abuse of hiding other costs. For example if you take out a $100 loan at 12% (one single repayment) but 5 points are charged. Then you get $100, but you only get $95 as the other $5 is your 5% points of $100) So actually you’ve borrowed $95 but must repay $112 at year end so your APR is not 12% but 112/95 -1 = 17.89%. You’d have the same APR if you made $1 interest payments each month and repaid at year end.