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48/3335–8FE Reference Handbook 10.4 · Engineering Economics · Effective rates
1. Simple Interest2. Single-Payment Compound Amount (F/P)3. Single-Payment Present Worth (P/F)4. Uniform-Series Compound Amount (F/A)5. Sinking-Fund Factor (A/F)6. Capital-Recovery Factor (A/P)7. Uniform-Series Present Worth (P/A)8. Effective Interest Rate9. Arithmetic Gradient Present Worth (P/G)10. Net Present Worth11. Benefit–Cost Ratio12. Straight-Line Depreciation13. Geometric Gradient Present Worth14. Capitalized Cost (Perpetual PW)15. Payback Period16. Break-Even Quantity17. Equivalent Uniform Annual Worth18. Internal Rate of Return vs MARR19. MACRS Depreciation20. Declining-Balance Depreciation21. Inflation and Real Interest22. Expected Value of Alternatives

Handbook formula

Effective Interest Rate

r is the nominal annual rate, m the number of compounding periods per year. ie is the effective annual rate. Continuous compounding uses e^r − 1.

Nominal annual rate
Compounds per year
Effective annual rate

Step-by-step solved example

Nominal 12% compounded monthly. Find the effective annual rate.

P12345An
Nominal vs effective rate on the same cash-flow axis.

  1. 1. Identify

    r = 0.12, m = 12.

  2. 2. Effective

    ie = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 = 0.1268 = 12.68%.

Answer: 12.68% per year

10 practice questions

0/10 correct

1.12% compounded quarterly has m =

2.Effective rate for 12% compounded quarterly is nearest

3.For a given r, increasing m makes ie

4.If compounding is annual, ie equals

5.Continuous compounding of 10% nominal gives ie nearest

6.Period rate when r = 12% monthly compounding is

7.APR quoted without compounding frequency is treated as

8.(1 + r/m)^m − 1 is independent of

9.6% compounded semiannually → ie nearest

10.Compare alternatives with different compounding using