Let's say you wish to retire in 35 years. Also, let's assume a constant APR of 9% compounded monthly. (NOTE: to get this kind of average yield, we're talking investing in nearly 100% stocks as a retirement account option. This is not at all uncommon, especially if you have a long time to go until retirement and can handle massive fluctuations).

It takes you 3 years to actually open the account.

If you were to make $350 monthly contributions to this retirement account, how much less will you have at retirement than if you had actually opened that account 3 years ago? Provide details on your calculation.

Secondly, suppose that you could go back in time and make a lump sum payment when you started saving for retirement to account for that deficiency of opening the account 3 years later than you had hoped. What "lump sum" deposit would you have needed to make at that three year mark to account for the deficiency, so that youd have the SAME amount in your account after 35 years (still assuming $350 monthly contributions). Provide details on your calculation.

If all you did to account for this deficiency was to adjust your monthly deposit to make what you should have had if you invested for the full 35 years, how much higher would this payment need to be? How much more will you have paid by going with this tactic? Provide details on your calculations.