Skip to main content

Nominal and effective rate for perpetual withdrawals

Short answer

Nominal rate ignores intra-year compounding; effective rate includes it. For a deposit of Rs 1,00,000 yielding Rs 1,000 per month forever: nominal annual rate = 12%, effective annual rate = 12.68%.

Differentiate between nominal and effective interest. Calculate both nominal and effective annual interest if you deposit now Rs 1,00,000 and you can draw Rs 1000 per month forever.

Nominal vs effective interest

PointNominal rate (r)Effective rate (i)
MeaningStated yearly rate, ignoring compounding within the yearActual yearly rate including compounding
CompoundingNot reflectedFully reflected
Formular = m × (rate per period)i = (1 + r/m)^m − 1
Example12% compounded monthly12.68% per year
Relationr ≤ i (equal only when m = 1)i ≥ r

Numerical

Withdrawals continue forever, so the deposit works as a perpetuity: P = A / i.

 P = 1,00,000 at t = 0;   1000 drawn at the end of every month, forever
  • Interest per month i = A / P = 1,000 / 1,00,000 = 0.01 = 1% per month
  • Nominal annual rate r = 12 × 1% = 12% per year (compounded monthly)
  • Effective annual rate i = (1 + 0.01)^12 − 1 = 1.12683 − 1 = 12.68% per year

Answer: nominal = 12% per year; effective = 12.68% per year.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Engineering Economics chapter 2 questions →