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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

An investor places 10,000 in an account earning 6% per annum, compounded continuously. How many years are needed for the balance to reach 15,000?

It takes about 6.76 years. With continuous compounding the balance grows by e raised to 0.06 times T, so T equals the natural log of 1.5 divided by 0.06. Annual compounding, simple interest, or doubling time give different, incorrect answers.

  1. A6.76Correct
  2. B6.96
  3. C8.33
  4. D11.55

Explanation

Solve 10,000 e^(0.06T) = 15,000, so T = ln(1.5)/0.06 = 0.405465/0.06 = 6.76 years. The 6.96 option uses annual compounding, ln(1.5)/ln(1.06). The 8.33 option uses simple interest, 0.5/0.06. The 11.55 option is the doubling time, ln(2)/0.06.

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