FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
An investment grows at a continuously compounded rate of 5% per year. Approximately how many years will it take to triple in value?
It takes about 21.97 years to triple. With continuous compounding at 5%, value grows as e to the power 0.05t, so tripling requires t equal to the natural log of 3 divided by 0.05. The natural log of 3 is about 1.0986.
- A13.86 years
- B21.97 yearsCorrect
- C22.52 years
- D40.00 years
Explanation
Solve e^(0.05t) = 3, so t = ln(3)/0.05 = 1.0986/0.05 = 21.97 years. The 22.52 answer uses annual compounding (ln3/ln1.05). The 13.86 answer is the doubling time, ln2/0.05. The 40.00 answer uses 2/0.05, ignoring the logarithm.
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