Mathematics
Assertion (A): Two friends invest the same amount of money for the same time (> 2 years) at the same rate of interest. One earns simple interest, but the other earns compound interest. Then both will get the same amount of money back at the end of investment.
Reason (R): The principal for each conversion period increases for the compound interest calculation.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Compound Interest
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Answer
Simple interest is calculated only on the original principal amount. The interest earned each period remains constant.
Compound interest is calculated on the original principal amount + all accumulated interest from previous periods. This means the principal for calculating interest increases with each conversion period.
The person earning compound interest will always have a higher amount back at the end of the investment period, if the conversion period is greater than one.
∴ Assertion (A) is false.
The principal for each conversion period increases for the compound interest calculation. This is true and is the fundamental principle of compound interest.
∴ Reason (R) is true.
∴ Assertion (A) is false, Reason (R) is true.
Hence, option 2 is the correct option.
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Related Questions
Consider the following two statements.
Statement 1: A sum of ₹ 1,000 invested at 10% p.a. rate of interest will earn ₹ 100 interest in first year.
Statement 2: Simple and compound interest is the same for first conversion period at the same rate of interest.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): The population of a town in 2015 was 10,000. It grew by 10% every year. So, in the year 2020, the population was 15,000.
Reason (R): Formula used in such problems is V = Vo
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
₹10000 was lent for one year at 10% per annum. By how much more will the interest be, if the sum was lent at 10% per annum, interest being compounded half-yearly?
A man invests ₹3072 for two years at compound interest. After one year the money amounts to ₹3264. Find the rate of interest and the amount due at the end of 2nd year.