Sonika invested an amount of ₹ 5800 for 2 years. At what rate of compound interest ( % per annum )

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6.Interest

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Sonika invested an amount of ₹ $5800$ for $2$ years. At what rate of compound interest ($\%$ $per$ $annum$) will she get an amount of ₹ $594.5$ at the end of two years?

A

$5$

B

$4$

C

$6$

D

$8$

Solution

(a) $594.5=5800\left[\left(1+\frac{r}{100}\right)^{2}-1\right]$

$\frac{594.5}{5800}=\left(1+\frac{r}{100}\right)^{2}-1$

$0.1025+1=\left(1+\frac{r}{100}\right)^{2}$

$1.1025=\frac{(100+r)^{2}}{10000}$

$1.1025 \times 10000=(100+r)^{2}$

$11025=(100+r)^{2}$

$(105)^{2}=(100+r)^{2}$

$105=100+r$

$r=5 \%$

Standard 13

Quantitative Aptitude

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