How are the present value and the future value of a lump sum related in definition and

Question:

How are the present value and the of a lump sum related in definition and in terms of mathematics? Notice that for a given interest rate (r) and a given investment time horizon (n), PVFr,n and FVFr,n are inverses of each other. Why?
Future Value
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value (FV) is important to investors and financial planners as they use it to estimate how much an investment made today will be worth...