Question

*In how many years the amount for Rs. 10000 becomes Rs. 12100 at 10% compound interest?*

1️⃣ 1
2️⃣ 2
3️⃣ 3
4️⃣ 4​

Answer 1

QUESTION -: *In how many years the amount for Rs. 10000 becomes Rs. 12100 at 10% compound interest?*

ANSWER -:

An amount of Rs 10000 becomes Rs 14641 in 2 years.

Answer 2

Answer:

$\large \underline\red{\sf \pmb{Given}}$

• ➛ Amount = Rs.12100
• ➛ Principle = Rs.10000
• ➛ Rate of Interest = 10%

$\large \underline \red {\sf \pmb{To \: Find }}$

• ➛ Time

$\large \underline{ \red {\sf \pmb{Using \: Formula}}}$

$\circ\underline{ \boxed{\bf \purple{A = P {\bigg(1 + \dfrac{R}{100} \bigg)}^{T} }}}$

Where

• ➟ A = Amount
• ➟ P = Principle
• ➟ R = Rate of Interest
• ➟ T = Time

$\large \underline \red{\sf \pmb{Solution}}$

$\begin{gathered} \implies{\sf{A = P {\bigg(1 + \dfrac{R}{100} \bigg)}^{T} }}\end{gathered}$

• ➛ Substituting the values

$\begin{gathered}\implies{\sf{12100 = 10000{\bigg(1 + \dfrac{10}{100} \bigg)}^{T} }}\end{gathered}$

$\begin{gathered}{ \implies{\sf{12100 = 10000{\bigg(\dfrac{100 + 10}{100} \bigg)}^{T} }}}\end{gathered}$

$\begin{gathered}{ \implies{\sf{ \dfrac{12100}{10000} = {\bigg(\dfrac{110}{100} \bigg)}^{T} }}}\end{gathered}$

$\begin{gathered}{ \implies{\sf{ \dfrac{121}{100} = {\bigg(\dfrac{11}{10} \bigg)}^{T} }}}\end{gathered}$

$\begin{gathered}{ \implies{\sf {{ \dfrac{11}{10}}^{2} = {\bigg(\dfrac{11}{10} \bigg)}^{T} }}}\end{gathered}$

$\begin{gathered}\implies \bf{T=2 \: years }\end{gathered}$

$\begin{gathered} \large \star \underline{\boxed{\bf \purple{Time=2 \: years }}}\end{gathered}$

• ➛ Henceforth,The amount for Rs. 10000 becomes Rs. 12100 at 10% in 2 years.

$\large \underline {\red{ \sf \pmb{Know \: More }}}$

★ Formula of Simple Interest (S.I)

• $: \implies\sf \purple{S.I = \dfrac{P \times R \times T}{100}}$

★ Formula of Principle(P) if Amount and Interest given

• $: \implies\sf \purple{P=Amount - Interest}$

★ Formula of Principle (P) if Interest,time and rate given

• $: \implies\sf \purple{P = \dfrac{Interest \times 100 }{Time \times Rate} }$

★ Formula of Principle (P) if amount,time and rate given

• $: \implies\sf \purple{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)} }$

★ Formula of Amount if Principle (P) and Interest (I) given

• ${: \implies \sf \purple{Amount = Principle + Interest }}$