What is the compound interest on a sum of ₹4,096 at 15% p.a. for $$2\frac{1}{2}$$ years, if the interest is compounded 10-monthly?

Given that the sum amount=Rs 4,096

Rate of interest$$=15\%$$pa

time$$=2\frac{1}{2}=\dfrac{5}{2}$$ year

So, total number of month $$=\dfrac{5\times 12}{2}=30$$month

so total of 10 month $$(n)= 3$$

Hence, rate of interest compounded per 10month $$r=\dfrac{15\times10}{12}=\dfrac{25}{2}\%$$

Now, $$A=P(1+\dfrac{r}{100})^n$$

Substituting the values,

$$\Rightarrow A=4096(1+\dfrac{25}{2\times100})^3$$

$$\Rightarrow A=4096(1+\dfrac{1}{8})^3$$

$$\Rightarrow A=4096(\dfrac{9}{8})^3$$

$$\Rightarrow A=4096\times\dfrac{9}{8}\times\dfrac{9}{8}\times\dfrac{9}{8}$$

$$\Rightarrow A=8\times 9\times9\times9=5832$$ Rs.

Hence, the required interest $$=5832-4096=1736Rs.$$