The difference between compound interest and simple interest on an amount of &#x

Question

The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. What is the rate of interest per annum?

Options:

A . 10%

B . 9%

C . 8%

D . 12%

Answer: Option C
:
C
Given that, principal,

P = ₹ 15000

and time period,

n = 2

years .
Let the rate of interest per annum be

r

.
Simple interest in 2 years

S . I = \frac{15000 \times r \times 2}{100}

\Rightarrow S . I = 300 r

Compound interest

C . I = A - P = 15000 (1 + \frac{r}{100})^{2} - 15000

, here,

A

is the amount.
Given that

C . I - S . I = 96

(Since C.I > S.I)

\Rightarrow 15000 (1 + \frac{r}{100})^{2} - 15000 - 300 r = 96

\Rightarrow 15000 (1 + \frac{r}{100})^{2} - 300 r = 15096

\Rightarrow 15000 (1 + \frac{r^{2}}{10000} + \frac{2 r}{100}) - 300 r = 15096

\Rightarrow 15000 + \frac{15 r^{2}}{10} + 300 r - 300 r = 15096

\Rightarrow \frac{15 r^{2}}{10} = 96

\Rightarrow 15 r^{2} = 960

\Rightarrow r^{2} = 64

\Rightarrow r = \pm 8

∵

Rate of interest cannot be negative, so

r = 8 %

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