Consider the following statements:
If a sum of money is lent at simple interest, then
(A) money gets doubled in 5 years if the rate of interest is \(16\frac{2}{3}\%\).
(B) money gets doubled in 5 years if the rate of interest is 20%.
(C) money becomes four times in 10 years if it gets doubled in 5 years.
of these statements,
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) only
Under simple interest the interest is the same every year, \(\text{SI}=\frac{P\times R\times T}{100}\). Money doubles when the interest equals the principal, \(\text{SI}=P\), which gives \(R\times T=100\).
(A) money gets doubled in 5 years if the rate of interest is \(16\frac{2}{3}\%\). Incorrect. Doubling in 5 years needs \(R=\frac{100}{5}=20\%\). At \(16\frac{2}{3}\%\) the money doubles in \(100\div16\frac{2}{3}=6\) years, not in 5.
(B) money gets doubled in 5 years if the rate of interest is 20%. Correct. In 5 years the interest is \(\frac{P\times20\times5}{100}=P\), so the amount is \(2P\): the money has doubled.
(C) money becomes four times in 10 years if it gets doubled in 5 years. Incorrect. Doubling in 5 years means an interest of \(P\) every 5 years. In 10 years the interest is \(2P\), so the amount is \(3P\), only three times; four times needs an interest of \(3P\), which takes 15 years.