Question

the sum of money that will yield ₹400 as compound interest at 5% pa compounded yearly for I year is​

Answer 1

Step-by-step explanation:

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

• Compound Interest = ₹400

• Rate of interest = 5%

• Time = 1 year.

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

• The sum of money ( Principal )

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

As we know that:-

$\boxed{ \rm \leadsto Amount = P\bigg({1 + \frac{r}{100} } \bigg)^{n} }$

Here:-

• P = Principal

• r = rate of interest = 5%

• n = time = 1 year

Substituting the values:-

$\rm \implies A= P \bigg({1 + \dfrac{5}{100} } \bigg)^{1}$

$\rm \implies A= P \bigg({ \dfrac{100 + 5}{100} } \bigg)$

$\rm \implies A= P \bigg({ \dfrac{105}{100} } \bigg)$

$\rm \implies A= P \bigg({ \dfrac{21}{20} } \bigg)$

$\rm \implies A= { \dfrac{21P}{20} } ......(i)$

Now:;

$\boxed{\rm \implies A - P=C.I}$

( Here:- CI = Compound Interest = ₹400)

From(i)

$\rm \implies \dfrac{21P}{20} - P=400$

$\rm \implies \dfrac{21P - 20P}{20} =400$

$\rm \implies \dfrac{P}{20} =400$

$\rm \implies {P} =400 \times 20$

$\rm \implies {P} =8000$

$\boxed{ \rm \therefore \: Sum \: of \: money =Rs.8000}$