Present & Future Value

Money today can earn returns, so it's worth more than the same sum later. Future value grows it forward with interest; present value discounts a future sum back at a required return.

Interest-on-interest accrues each period, so monthly compounding slightly beats annual at the same nominal rate. The effect is small next to the rate itself.

FV = PV×(1+r)^n for a lump sum; contributions add PMT×(((1+r)^n−1)/r). Present value runs the same math backwards.

Your required return — often a safe rate for valuing guaranteed cash, or a higher hurdle for risky ones. The answer is very sensitive to it.

Compounding is exponential: over decades, returns on returns snowball past what you put in. Starting early beats contributing more later.

No. Planning estimates only — real investing carries risk this math ignores.