Question

at what rate percent will a sum of rupees 1,000 amount to 1100 2.50 in 2 years at compound interest​

Answer 1

$\small\sf\colorbox{black}{ \colorbox{white}{\colorbox{white}{Correct question}}}$

At what rate percent will a sum of rupees 1,000 amount to 1102.5 in 2 years at compound interest

Solution :-

$\star$ Given :

• Principal = Rs.1000

• Amount = Rs. 1102.5

• Time = 2 years

$\star$To Find :

• $\small\sf\colorbox{black}{ \colorbox{red}{\colorbox{white}{Rate\:%}}}$

Solution :

Let the rate of interest = R % per annum. So,

$\huge\sf\implies$ A = P [( 1 + $\frac{R}{100}$)^t

$\huge\sf\implies$ 1000 [ 1 + $\huge\sf\frac{R}{100}$ ]²

$\huge\sf\implies$ 1102.50 = (1 + $\huge\sf\frac{R}{100}$ )²

$\huge\sf\implies$ $\huge\sf\frac{1102.50}{1000}$

$\huge\sf\implies$ $\huge\sf\frac{4410}{4000}$

$\huge\sf\implies$($\huge\sf\frac{21}{20}$)²

$\huge\sf\implies$1 + $\huge\sf\frac{R}{100}$

$\huge\sf\implies$ $\huge\sf\frac{21}{20}$

$\huge\sf\implies$ $\huge\sf\frac{R}{100}$

$\huge\sf\implies$ $\huge\sf\frac{21}{20}$ - 1

$\huge\sf\implies$ $\huge\sf\frac{1}{20}$

$\huge\sf\implies$ R

$\huge\sf\implies$ $\huge\sf\frac{1}{20}$ × 100

$\huge\sf\implies$ 5 %

Hence, Rate percentage is 5%

$\huge\sf\color{red} {More\: Information}$

• The amount of money lent or borrowed is called the principal.

• The additional money charged for its use is called Interest

• If the interest due is added to the principal,the total money we receive or pay is called amount due at time

Important formulae :

$\colorbox{black}{\colorbox{white}{\colorbox{white}{Amount\:= \: principal\:+\:Interest}}}$

Interest = $\frac{Principal×Rate×time}{100}$

Rate = $\frac{Interest×100}{Principal×time}$

Time = $\frac{Interest×100}{Principal×rate}$