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 Hint: First, we will let the principal sum of money as ‘P’ and the rate of interest as ‘R’. we will use the conditions given in the question and formula of compound interest to form a different equation. And by solving those equations we will find the rate of interest. Complete step-by-step solution: Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
Correct Answer:
Description for Correct answer: \( \Large 1 \rightarrow\ \ 4 \) \( \Large 4=1 \left(1+\frac{r}{100}\right)^{2}\) \( \Large 4= \left(1+\frac{r}{100}\right)^{2}\) r = 100 % Part of solved Simple and compound interest questions and answers : >> Aptitude >> Simple and compound interest A. 100% B. 75% C. 50% D. 20% Solution(By Examveda Team)$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,{\text{1}}\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\,\,\,{\text{4}} \cr & \Rightarrow 4 = 1{\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow 4 = {\left( {1 + \frac{r}{{100}}} \right)^2} \cr & \Rightarrow r = 100\% \cr & \cr & {\text{Alternate}} \cr & {\text{Principal}}\,\,\,\,\,\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,\,\,\root 2 \of 1 \,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\root 2 \of 4 \cr & \,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,2 \cr & \Rightarrow {\text{Rate of interest}} \cr & {\text{ = }}\frac{{\left( {2 - 1} \right)}}{1} \times 100 = 100\% \cr} $$ Let Principal (P) = Rs. 100 then Amount (A) = Rs. 400 Period (n) = 2 years or 4 half years. Let R be the rate % half-yearly, then AP=(1+R100)n⇒400100=(1+R100)4 ⇒(1+R100)4=41 ⇒[(1+R100)2]2=(2)2 ⇒(1+R100)2=2⇒(1+R100)=√2 ⇒1+R100=1.4142 ⇒R100=1.4142−1.0000 ⇒R100=0.4142⇒R=0.4142×100 ⇒R=41.42 ∴ Rate %=41.42% half yearly and 82.84% p.a.At what rate of compound interest does a sum of money becomes 4 times of itself in 4 years?∴ Rate %=41.42% half yearly and 82.84% p.a.
In what time does a sum of money become 4 times?A sum of money become four times at the simple interest rate of 5% per annum in 60 years . Formula : Hence a sum of money become four times at the simple interest rate of 5% per annum in 60 years .
At what rate percent per annum a sum of money becomes four times of itself in 15 years?∴ The rate of interest is 20%. ∴ The rate of interest is 20%.
At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years select one a 100% B 50% C 60% D 25%?The rate of interest is 50 % per annum.
Here, a sum of money becomes 9/4 of itself in 2 years.
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At what rate of compound interest does a sum of money becomes 4 times of itself?
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