A perfect round trip: forward, then back
₹1,00,000 growing at 8% for 10 years reaches a real ₹2,15,892.50, computed by the future value calculator. Feeding that exact ₹2,15,892.50 into the present value calculator, with the identical 8% rate and 10-year period, returns exactly ₹1,00,000 — the original amount, with zero rounding loss.
Why this isn't a coincidence
Future value multiplies by (1 + rate)^years, and present value divides by that same factor — multiplying and then dividing by the identical number always returns the original starting point, provided the rate and years used in both directions match exactly. This is the algebraic definition of "inverse operations," not an approximation.
What breaks the round trip: a mismatched rate
Discounting that same ₹2,15,892.50 back using a 10% rate instead of the original 8% returns only ₹83,235.90 — noticeably less than the original ₹1,00,000. The round trip only returns the exact starting value when the same rate is used in both directions; a different discount rate answers a different question entirely (what that future amount is worth under different assumptions about the cost of money).
Why this matters when picking a discount rate
This round trip is a useful sanity check when working with time-value-of-money calculations: if a future amount was itself projected using a specific growth rate, discounting it back with anything other than that same rate is a deliberate choice — often the right one, since your actual opportunity cost of capital may differ from the original growth assumption — not a mistake, but one that should be made consciously rather than by accident.