Since English is not my mother tongue, please bear with me on this.

Given the below 2 paragraphs, what’s the difference between “A lump sum with interim cash” and “A lump sum with no interim cash”?

The Future Value of a Lump Sum with Interim Cash Reinvested at the Same Rate

You are the lucky winner of your state’s lottery of $5 million after taxes. You invest your winnings in a five-year CD at a local financial institution. The CD promises to pay 7%/year compounded annually. This institution also lets you reinvest the interest at that rate for the duration of the CD.

The Future Value of a Lump Sum with No Interim Cash

For an investment of $2,500,000, an institution promises to pay you a lump sum 6 years from now at an 8% annual interest rate.

in each period with interim cash option - you get an inflow of some amount of cash - that you can reinvest - as stated in the first part - either at the original rate - or at some other different rate.

in the with no interim cash situation - over the lifetime of the investment - you get no other cash - what you invested in the very beginning is all that the investment has.

What makes this still confusing to me is the fact that we use the exact same formula to calculate FV (since compounding frequency is 1 for both)

FV = PV (1+I/Y)^N

also, in both situation you dont “get” any inflow. Your initial investment simply earns interest in both situations. I still do not see the difference between “interm” and “no interm” maybe this example is a bad one and I should look for more contrasted situations. I hope you see where the confusion is for me.