Question

1000 रूपये रकमेवरील 5% दराने 2‌ वर्षासाठी सरळव्याज आणि चक्रवाढव्याज यातील फरक किती रूपये असेल translate in English​

Answer 1

In English: What is the difference between simple interest and compound interest for 2‌ years at the rate of 5% on the amount of Rs.1000 ?

$\\ {\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• Principal = ₹1000
• Rate (r) = 5%
• Time (t) = 2 years

$\circ \ {\pmb{\underline{\boxed{\sf{ Interest_{(Simple)} = \dfrac{PRT}{100} }}}}} \\ \\ \\ \colon\implies{\sf{ \dfrac{10 \cancel{00} \times 5 \times 2}{ \cancel{100} } }} \\ \\ \\ \colon\implies{\sf{ 10 \times 5 \times 2 }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf{ Rs. \ 100_{(Simple \ Interest)} }}}}$

Now, We've to find the compound interest but Firstly we've to find Amount of the transaction as:-

$\circ \ {\pmb{\underline{\boxed{\sf{ Amount = P \left( 1 + \dfrac{r}{100} \right)^n }}}}} \\ \\ \\ \colon\implies{\sf{ 1000 \left( 1 + \dfrac{5}{100} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ 1000 \left( \cancel{ \dfrac{105}{100} } \right)^2 }} \\ \\ \\ \colon\implies{\sf{ 1000 \left( \dfrac{21}{20} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ \cancel{1000} \times \dfrac{21}{ \cancel{20} } \times \dfrac{21}{ \cancel{20} } }} \\ \\ \\ \colon\implies{\sf{ 2.5 \times 21 \times 21 }} \\ \\ \\ \colon\implies{\sf{Rs. \ 1102.5_{(Amount)} }}$

As we know that:

$\colon\implies{\sf{ Interest = Amount - Principal }} \\ \\ \colon\implies{\sf{ 1102.5 - 1000 }} \\ \\ \colon\implies{\underline{\boxed{\sf{ Rs. \ 102.5_{(Compound \ Interest)} }}}}$

So, The Compound Interest is ₹102.5

~ Now, We can Calculate the difference b/w Simple Interest and Compound Interest as:-

$\colon\mapsto{\sf{ 102.5 - 100 }} \\ \\ \colon\mapsto{\sf{ Rs. \ 2.5 _{(Difference)} }}$

Hence,

The difference b/w simple interest and compound interest is ₹2.5 .