FRM Part I · FRM Exam Part I · Properties of Interest Rates
An investor deposits 10,000 at a continuously compounded rate of 4% per annum. What is the value after 18 months, to the nearest unit?
The deposit grows to about 10,618. With continuous compounding the value is 10,000 times e raised to 0.04 times 1.5, which is e to 0.06, about 1.0618. Simple interest would give only 10,600, understating the growth.
- A10,618Correct
- B10,600
- C10,605
- D10,408
Explanation
Value = 10,000 × e^(0.04×1.5) = 10,000 × e^0.06 = 10,000 × 1.061837 = 10,618. The 10,600 option uses simple interest (4% × 1.5). The 10,408 option uses only one year of growth.
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