Simple and compound interests on a sum of money for 2 years are ₹ 8400 and ₹ 8652 respectively.

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6.Interest

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The simple and compound interests on a sum of money for $2$ years are ₹ $8400$ and ₹ $8652$ respectively. The rate of interest per annum is (In $\%$)

A

$6$

B

$7.5$

C

$9$

D

$4.5$

Solution

(a) Quicker Method:

For 2 years

$\because$ simple interest $=\frac{200 \times \text { Rate }}{\text { Rate }(\text { Rate }+200)} \times$ CI

$\Rightarrow 8400=\frac{200 r}{r(r+200)} \times 8652$

$\Rightarrow 8400\left(r^{2}+200 r\right)=8652 \times 200 r$

$\Rightarrow 8400 r^{2}=(8652-8400) \times 200 r$

$\Rightarrow 42 r=252$

$\therefore r=6 \%$

Standard 13

Quantitative Aptitude

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