At what rate percent Compound interest per annum will be Rs 640 amount to Rs 774.40 in two years

At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years?

Let the rate of interest be R % .Then, \[A = P \left( 1 + \frac{R}{100} \right)^n \]\[774 . 40 = 640 \left( 1 + \frac{R}{100} \right)^2 \]\[ \left( 1 + \frac{R}{100} \right)^2 = \frac{774 . 40}{640}\]\[ \left( 1 + \frac{R}{100} \right)^2 = 1 . 21\]\[ \left( 1 + \frac{R}{100} \right)^2 = \left( 1 . 1 \right)^2 \]\[\left( 1 + \frac{R}{100} \right) = 1 . 1\]\[\frac{R}{100} = 0 . 1\]R = 10

Thus, the required rate of interest is 10 % per annum.

Concept: Rate Compounded Annually Or Half Yearly (Semi Annually)

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At what rate percent compound interest per annum will rs. 640 amount to Rs. 774.40 in 2 years?

Solution

Principal (P) = Rs. 640 Amount (A) = Rs. 774.40

Rate (R) $=10\%$ p.a

Period (n) = 2 years Let R be the rate of interest p.a.

$\therefore \frac{A}{P}={(1+\frac{R}{100})}^n$

$\Rightarrow \frac{774.40}{640}={(1+\frac{R}{100})}^2$
$\Rightarrow \frac{77440}{100\times 640}={(1+\frac{R}{100})}^2$
$\Rightarrow \frac{121}{100}={(1+\frac{R}{100})}^2$ (Dividing by 640)
$\Rightarrow {\left(\frac{11}{10}\right)}^2={(1+\frac{R}{100})}^2$ Comparing, we get

$1+\frac{R}{100}=\frac{11}{10}=1+\frac{1}{10}$

$\therefore \frac{R}{100}=\frac{1}{10}\Rightarrow R=\frac{100}{10}=10$
$\therefore$ Rate $=10\%$ p.a

Mathematics

RD Sharma

Standard VIII