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CA FOUNDATION: QUANTITATIVE APTITUDE · TIME VALUE OF MONEY

Effective rate of interest

Effective annual rate E = (1 + r/m)^m − 1, where r is the nominal rate and m the compounding periods per year.

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Worked examples

Example 1 · level 1

A bank offers 12% p.a. compounded half-yearly. What is the effective annual rate of interest? (Answer in %, two decimals.)

Show solution
  1. Rate per period = 12 ÷ 2 = 6%.
  2. (1 + 0.06)^2 = 1.1236.
  3. E = 1.1236 − 1 = 12.36%.

Answer: 12.36 %

Example 2 · level 2

A bank offers 12% p.a. compounded quarterly. What is the effective annual rate of interest? (Answer in %, two decimals.)

Show solution
  1. Rate per period = 12 ÷ 4 = 3%.
  2. (1 + 0.03)^4 = 1.1255.
  3. E = 1.1255 − 1 = 12.55%.

Answer: 12.55 %

Example 3 · level 3

A bank offers 16% p.a. compounded quarterly. What is the effective annual rate of interest? (Answer in %, two decimals.)

Show solution
  1. Rate per period = 16 ÷ 4 = 4%.
  2. (1 + 0.04)^4 = 1.1699.
  3. E = 1.1699 − 1 = 16.99%.

Answer: 16.99 %

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