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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Investment

An investment of Rs 1,000 grows to Rs 1,200 in year 1 and then falls to Rs 1,080 at the end of year 2, with no cash flows in between. Which is the correct compound annual growth rate (CAGR) over the two years, approximately?

CAGR is approximately 3.92 percent. The investment grew from Rs 1,000 to Rs 1,080, a total of 8 percent, so the annual compounded rate is the square root of 1.08 minus one. The arithmetic average of 5 percent overstates it.

  1. AExactly 4%
  2. BExactly 8%
  3. CApproximately 3.92%Correct
  4. DApproximately 5%

Explanation

CAGR = (1,080/1,000)^(1/2) - 1 = (1.08)^0.5 - 1 = 1.0392 - 1 = about 3.92%. The arithmetic average of returns (20% and -10%) is 5%, which overstates growth. 4% is simply 8% divided by 2. 8% is the total return, not annual.

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