Say that you are trying to have $113,838.66 saved up in 13 years for college tuition. There are three options to save up for it:

1. Save $417.11 per month for the next 156 months. 2. Save $425.38 per month for the next 12 months. Transfer that Future Value into a separately managed account at the end of the first year. Repeat this for the next 13 years. 3. Borrow the Present Value of $113,838.66, (which is $41,858.24) and Invest that for 13 years to achieve a future value of $113,838.66 to pay for college. Repay this loan by paying $432.43 per month afterwards

After calculating each scenario in Excel, I realized that:

Option 1 over saves by $0.94

Option 2 costs an extra $8.27 per month over option 1 and over-achieves the goal by $0.85 (9 cents less than option 1), which means it has a slightly lower Future Value

Option 3 costs an extra $15.31 per month over option 2 and has a slightly higher future value than Option 1 after 13 years

My question is:

Can someone explain the payment options and why the payments are so far apart from each other, shouldnt they only be about a penny away from each other? And why are the monthly payments so far apart? Or are my calculations incorrect?

Thank you in advance.