**Question:**

Abhay borrowed Rs 16000 at $7 \frac{1}{2} \%$ per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?

**Solution:**

Principal amount, $P=$ Rs 16000

Rate of interest, $R=\frac{15}{2} \%$ p. a.

Time, $n=2$ years

Now, simple interest $=$ Rs $\left(\frac{16000 \times 2 \times 15}{100 \times 2}\right)=$ Rs. 2400

Amount including the simple interest $=$ Rs $(16000+2400)=$ Rs 18400

The formula for $t h e$ amount including the compound interest is given below:

$\mathrm{A}=P\left(1+\frac{R}{100}\right)^{\mathrm{n}}$'

$=$ Rs. $16000\left(1+\frac{15}{100 \times 2}\right)^{2}$

$=$ Rs. $16000\left(1+\frac{15}{200}\right)^{2}$

$=$ Rs. $16000\left(1+\frac{3}{40}\right)^{2}$

$=$ Rs. $16000\left(\frac{40+3}{40}\right)^{2}$

$=$ Rs. $16000\left(\frac{43}{40}\right)^{2}$

$=$ Rs. $16000(1.075 \times 1.075)$

i.e., the amount including the compound interest is Rs 18490 .

Now, $(\mathrm{CI}-\mathrm{SI})=\mathrm{Rs} .(18490-18400)=$ Rs. 90

Therefore, Abhay gains Rs. 90 as profit at the end of 2 years.

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