The question below consists of a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.
What is the rate of the compound interest?
Statement I: A sum of 1000 amounts to 1331 at the rate of compound interest.
Statement II: The amount was invested for the period of three years.
Statement III: The simple interest received on that amount in one year is equal to the compound interest received on that amount in the first year.
Options:
A) The data in statements I and II together are sufficient to answer the question, while the data in statement III are not sufficient to answer the question.
B) The data in statements I and III together are sufficient to answer the question, while the data in statement II are not sufficient to answer the question.
C) The data in statement I, II and III together are not sufficient to answer the question.
D) The data in statement I only and II together or only statement III are sufficient.
E) The data in all the statements I, II and III together are necessary to answer the question.
Right Answer: A) Statement I and II together.
- From Statement I, II combined we can find the Rate of Interest.
- Statement III is redundant/tautological because simple interest for 1 year = compound interest for 1st year is always true, adding no new information.Combining Statement I and II:
- We have P = 1000, A = 1331, and T = 3.
- Using the formula A = P(1 + R/100)^T:
- 1331 = 1000(1 + R/100)^3
- 1.331 = (1 + R/100)^3
- Taking the cube root of both sides:
- 1.1 = 1 + R/100
- 0.1 = R/100
- R = 10%
- Together, I and II are sufficient.
