Discussion
Which of the following is/are correct?
1. If a sum doubles in 10 years at simple interest, the rate of interest is 10% per annum.
2. If a sum doubles in 10 years at compound interest, the rate of interest must be more than 10% per annum.
Select the answer using the code given below:
Answer: A
1 only is correct.
Statement 1: at simple interest, doubling means the interest equals the principal: \(P \times r \times 10 / 100 = P\), so r = 10%. True.
Statement 2: at compound interest, \((1 + r)^{10} = 2\) gives \(r \approx 7.2\%\), since the interest itself earns interest. The rate needed is less than 10%, not more; at 10% compound a sum would grow to about 2.59 times in 10 years. False.
The rule of 72 gives the same answer quickly: \(72 / 10 \approx 7.2\%\).
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