The simple interest on Rs. 3640 for 3 years at a certain rate percent p.a. is Rs. 273. Find the compound interest of the same sum for the same time at the same rate of interest.

Solution

Step 1: Find the rate of interest (R)

The formula for Simple Interest (SI) is: $$SI=\frac{P\times R\times T}{100}$$ Given:

• $SI=273$
• $P=3640$
• $T=3$ years

Substitute the values: $$273=\frac{3640\times R\times 3}{100}$$ $$273=109.2\times R$$ $$R=\frac{273}{109.2}=2.5\%$$

Step 2: Calculate the Compound Interest (CI)

The formula for Compound Interest (CI) is: $$CI=P\times {\left(1+\frac{R}{100}\right)}^T-P$$ Substitute the values: $$CI=3640\times {\left(1+\frac{2.5}{100}\right)}^3-3640$$ $$CI=3640\times (1.025{)}^3-3640$$ Calculate $(1.025{)}^3$: $$(1.025{)}^3=1.076890625$$ Now, compute the CI: $$CI=3640\times 1.076890625-3640$$ $$CI=3913.20-3640=273.20(\text{rounded to 2 decimal places})$$

Final Answer: The compound interest is Rs. 273.20.