The sum of money that will yield ₹400 as compound interest at 5% pa

1.	The sum of money that will yield ₹400 as compound interest at 5% pa compounded yearly for I year is
Answer» 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:- $\boxed{ \rm \leadsto Amount = P\bigg({1 + \frac{<klux>R</klux>}{100} } \bigg)^{n} }$ 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) $\rm \implies \dfrac{21P}{20} - P=400$ $\rm \implies \dfrac{21P - 20P}{20} =400$ $\rm \implies \dfrac{P}{20} =400$ $\rm \implies {P} =400 \times 20$ $\rm \implies {P} =8000$ $\boxed{ \rm \therefore \: Sum \: of \: money =Rs.8000}$