- 2065 Kartik · 4 marks
Nominal vs effective rate; quarterly rate from monthly
Short answer
Nominal rate ignores compounding within a period; effective rate includes it. With 1% monthly, effective quarterly rate = (1.01)^3 - 1 = 3.0301% (nominal quarterly 3%).
Differentiate between nominal interest rate and effective interest rate. If monthly interest rate is 1%, what will be the quarterly interest rate?
Nominal vs effective interest rate
| Point | Nominal rate | Effective rate |
|---|---|---|
| Definition | Stated rate for a year (or period), not counting compounding inside it | Actual rate for the period after compounding |
| Calculation | r = rate per sub-period × m | i = (1 + r/m)^m − 1 |
| Compounding | Ignored | Included |
| Value | Lower (or equal) | Higher (or equal) |
| Example | 12% per year, compounded monthly | 12.68% per year |
| Use in formulas | Not used directly | Used in factors once period matches payment period |
Quarterly rate from monthly rate
Monthly rate = 1%, and a quarter has 3 months.
- Nominal quarterly rate = 3 × 1% = 3%
- Effective quarterly rate i = (1 + 0.01)^3 − 1 = 1.030301 − 1 = 3.0301%
Answer: the quarterly interest rate is 3.03% (effective); the nominal quarterly rate is 3%.
✓ Answer checked by Claude Opus 5.5 (high effort)
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