The GATE Grind

GATE 2021 CH – Question 24

Plant Design and Economics · Depreciation, rate of return, payback period and discounted cash flow · 1 mark · Multiple choice

A principal amount is charged a nominal annual interest rate of 10%. If the interest rate is compounded continuously, the final amount at the end of one year would be

  1. higher than the amount obtained when the interest rate is compounded monthly
  2. lower than the amount obtained when the interest rate is compounded annually
  3. equal to 1.365 times the principal amount
  4. equal to the amount obtained when using an effective interest rate of 27.18%

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) higher than the amount obtained when the interest rate is compounded monthly

Explanation

For continuous compounding, $A/P=e^{rt}=e^{0.10}=1.105170$. Monthly compounding at the same nominal rate gives $(1+0.10/12)^{12}=1.104713$, while annual compounding gives 1.10.

Thus continuous compounding gives a slightly **higher** amount than monthly compounding. Its effective annual rate is $(e^{0.10}-1)100=10.517\%$, not 27.18%. **Answer: A.**