CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
An investment of GBP 8,000 grows to GBP 12,000 over 5 years with annual compounding. The annual compound growth rate is closest to:
The compound annual growth rate is about 8.4%. Taking the fifth root of the 1.5 total growth multiple gives 1.0845. Simply dividing the 50% total gain by five years gives 10%, which ignores compounding and overstates the rate.
- A7.0%
- B8.4%Correct
- C10.0%
Explanation
r = (12,000/8,000)^(1/5) - 1 = 1.5^0.2 - 1. ln1.5 = 0.405465; /5 = 0.081093; exp = 1.0845, so r = 8.4%. Check: 1.0845^5 = 1.5. The 10.0% figure is the simple average (50%/5), which ignores compounding.
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