In what time will a sum of a money double itself at 6.25% per annum simple interest?
ANSWER
Verified
- Hint: In this question, we first need to get the relation between the principal and simple interest by using the formula involving the amount. Then by using the simple interest formula we can get the time. \[A=P+SI\] \[SI=\dfrac{P\times T\times R}{100}\]
Complete step-by-step solution -
SIMPLE INTEREST: If the interest is calculated on the original sum for any period of time, is called simple interest. \[SI=\dfrac{P\times T\times R}{100}\] Where, P is the principal, T is the time, R is the rate of interest and SI is the simple interest. AMOUNT: Principal together with the amount of interest is called amount. \[A=P+SI\] Now, from the given conditions in the question we have Let assume P as the principal amount and A as the amount. \[\Rightarrow A=2P\] Now, by substituting this value of A in the relation between A, P and SI we get, \[\begin{align} & \Rightarrow A=P+SI \\ & \Rightarrow 2P=P+SI \\ \end{align}\] Now, on rearranging the terms in the above equation and further simplifying we get, \[\begin{align} & \Rightarrow SI=2P-P \\ & \therefore SI=P \\ \end{align}\] Now, given in the question that \[\Rightarrow R=6.25=\dfrac{625}{100}\] Now, by substituting all these value in the simple interest formula we get, \[\begin{align} & \Rightarrow SI=\dfrac{P\times T\times R}{100} \\ & \Rightarrow P=\dfrac{P\times T\times 625}{100\times 100} \\ \end{align}\] Now, on cancelling the common terms on both the sides we get, \[\Rightarrow 1=\dfrac{T\times 625}{100\times 100}\] Now, on multiplying on both sides with 10000 we get, \[\Rightarrow 100\times 100=T\times 625\] Now, on dividing on both sides with 625 and further simplifying we get, \[\begin{align} & \Rightarrow T=\dfrac{100\times 100}{625} \\ & \therefore T=16\text{ years} \\ \end{align}\]
Note: It is important to note that the amount is twice the principal which gives us the simple interest in terms of principal. So, when we substitute in the simple interest formula we have T as the only unknown which on simplification gives the result. While calculating we should not neglect any of the terms because it changes the result completely. Instead of multiplying with 10000 on both sides and then dividing with 625 to get T we can directly do cross multiplication and then rearrange the terms which gives the same result.