Question

In how many years will a sum of Rs. 5,000 become Rs. 6,655 at the compound interest rate of 10% per annum?​

Answer 1

Answer:

this is the✅ answer for your question

Answer 2

Answer:

Step-by-step explanation:

${\large{\underline{\underline{\bf{Given \: : - }}}}}$

• ⟶ Amount = Rs.6655
• ⟶ Principle = Rs.5000
• ⟶ Rate of Interest = 10% per annum

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{To \: Find\: : - }}}}}$

• ⟶ Time

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Concept\: : - }}}}}$

★ Here we have given that the Principal is Rs.5000, Amonut is Rs.6655 and rate is 10% per annum. Here we need to find the time.

★So, we will find out the time by substituting the values in the formula.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Using \: Formula\: : - }}}}}$

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

Where

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

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Solution\: : - }}}}}$

★ Let us find out the Amount by Substituting the values in the formula :

${\dashrightarrow{\sf{A={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

• Substituting the values

${\dashrightarrow{\sf{6655={5000{\bigg(1 + \dfrac{10}{100}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{6655={5000{\bigg( \dfrac{(1 \times 100) + 10}{100}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{6655={5000{\bigg( \dfrac{100 + 10}{100}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{6655={5000{\bigg( \dfrac{110}{100}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{6655={5000{\bigg( \cancel\dfrac{110}{100}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{6655={5000{\bigg( \dfrac{55}{50}{\bigg)}^{T}}}}}}$

${\dashrightarrow{\sf{\dfrac{6655}{5000} = {\bigg( \dfrac{55}{50}{\bigg)}^{T}}}}}$

${\dashrightarrow{\sf{ \cancel\dfrac{6655}{5000} = {\bigg( \cancel\dfrac{55}{50}{\bigg)}^{T}}}}}$

${\dashrightarrow{\sf{\dfrac{1331}{1000} = {\bigg( \dfrac{11}{10}{\bigg)}^{T}}}}}$

${\dashrightarrow{\sf{{\bigg(\dfrac{11}{10}\bigg)}^{3} = {\bigg( \dfrac{11}{10}{\bigg)}^{T}}}}}$

${\dashrightarrow{\sf{{\bigg( {\cancel\dfrac{11}{10}}\bigg)}^{3} = {\bigg( \cancel{\dfrac{11}{10}}{\bigg)}^{T}}}}}$

$\dashrightarrow{\sf{Time = 3 \: years}}$

$\bigstar{\red{\underline{\boxed{\bf{Time = 3 \: years}}}}}$

∴ The time is 3 years.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Answer\: : - }}}}}$

• ⟶ In 3 years will a sum of Rs. 5,000 become Rs. 6,655 at the compound interest rate of 10% per annum.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Learn \: More\: : - }}}}}$

$\small\purple{\underline{\boxed{\bf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}$

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

$\small\purple{\underline{\boxed{\bf{Amount = Principle + Interest}}}}$

$\small\purple{\underline{\boxed{\bf{ Principle=Amount - Interest }}}}$

$\small\purple{\underline{\boxed{\bf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

$\small\purple{\underline{\boxed{\bf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

$\small\purple{\underline{\boxed{\bf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}$

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