The second picture was a chegg response. My question was initially why we took the present then future value for Darryl but we solved for the future value of Cheryl without having to calculate her present value. My professor says times zero is present value so in Cheryls case is times zero year 7 which is when her investment begins? Or is times zero from when she is age 22? If so why?

2/131201 Thc Power of compand intcio Daryl Choyl are 22 ycus oid. They cupect have an xa 8 2,00 g1 end of eash ycar to inver ov spend as tney chuc Chouci to Spend hcv B 3,ou ycan ou fur a tool of 37 anavsl hau meh dd Dany d Chesy Invar hou much du Incy have ar s? Danyi's IRA e 23 24 200 u Chowi's IRA For Darryl As he invested 2000 x 6 payments, there are two ways to calculate the FV at time 65 1. Either you get PV of all 6 payments at age 22, and then calculate FV for next 43 years ie (65 yrs - 22 Yrs). or 2. Calculate total Accumulated value of these 6 payments at time 6 i.e. when Darryl has completed his payments i.e. at age 28 years and then calculate i.e. (65 years - 28 years) the FV of the accumulated value for next 37 years For Cherryl, As there was no payment from her side till age 28, so there is no point to go back till age 22. Hence, Professor directly calculated the FV from age 28 till 65 i.e. 37 Years. As Way 1 was more easy than Way 2, hence your professor chose the easier one. (which i would have also gone for:))