Solution

Given:

Present value $$= ₹ 16000$$
Interest rate $$= 7\dfrac{1}{2} \% per annum $$= 15/2 \%$$
Time $$=2$$ years

To find the amount we have the formula,
Amount $$(A) = P (1+(r/100))^n$$
where $$P$$ is the present value, $$r$$ is the rate of interest, $$n$$ is time in years.

Now substituting the values in above formula we get,

$$\therefore A = 16000 (1 +(15/2)/100)^2$$
$$\Rightarrow A = 16000 (1+3/40)^2$$
$$\Rightarrow A =16000 (43/40)^2$$
$$\Rightarrow A = 16000 (1894/1600)$$
$$\Rightarrow A = ₹\ 18490$$

Now, we find the compound interest,
∴ Compound interest $$= A – P$$

$$= 18490 – 16000 = ₹\ 2490$$


Now we find the simple interest,


Simple interest $$(SI) = PTR/100$$
where $$P$$ is principle amount, $$T$$ is time taken, $$R$$ is rate per annum

$$SI = (16000 × (15/2) × 2) / 100$$

$$= 160 × 15$$

$$= ₹\ 2400$$



Abhay's gain at the end of $$2$$ years$$ = (CI – SI)$$

$$= 2490 – 2400$$
$$= ₹\ 90$$