I made some pretty unreasonable but convenient assumptions with the basic compound interest formula in back-of-the-envelope math to arrive at ~2.25% annual inte

I made some pretty unreasonable but convenient assumptions with the basic compound interest formula in back-of-the-envelope math to arrive at ~2.25% annual interest rate. http://www.wolframalpha.com/input/?i=compound+interest&a=*C.compound+interest-_*Formula.dflt-&a=FSelect_**PresentValueFutureValueDates-.dflt-&a=*FS-_**PresentValueFutureValueDates.i-.*PresentValueFutureValueDates.PV-.*PresentValueFutureValueDates.FV--&f4=19%2C600%2C000%2C000&f=PresentValueFutureValueDates.FV_19%2C600%2C000%2C000&f5=17%2C200%2C000%2C000&f=PresentValueFutureValueDates.PV_17%2C200%2C000%2C000&a=*FP.PresentValueFutureValueDates.compoundingfreq-_Monthly&f7=29+Dec+2008&f=PresentValueFutureValueDates.ID%5Cu005f29+Dec+2008&f8=17+Oct+2014&f=PresentValueFutureValueDates.MD%5Cu005f17+Oct+2014 http://www.wolframalpha.com/input/?i=compound+interest&a=*C.... Assumptions: - I know the amount was not dispersed all at once at the start - I have no idea what compounding frequency seems appropriate - Does not account for inflation - Time frame: 12/29/2008–10/17/2014 per the linked pdf [1] Aside: $17.2B 2008 dollars adjusted for inflation becomes $18.89B 2014 dollars. https://www.wolframalpha.com/input/?i=17%2C200%2C000%2C000+2008+dollars+in+2014 https://www.wolframalpha.com/input/?i=17%2C200%2C000%2C000+2... That makes the return a bit less exciting. I'd love to model this in a more accurate way if others know how that might be done. 1: https://www.treasury.gov/press-center/press-releases/Documents/Ally%20Financial%20Timeline.pdf https://www.treasury.gov/press-center/press-releases/Documen...