Given:
The amount after 2 years = ₹2700
The amount after 3 years = ₹3150
We need to find the rate of interest per annum (R).
Concept:
In simple interest, the interest accrued over a given time is constant for each year. The formula for the amount is:
Amount = Principal + Simple Interest
Simple Interest = Principal × Rate × Time / 100
Difference in amounts over one year equals the simple interest for one year.
Calculation:
Step 1: Calculate the simple interest for one year.
Interest for 1 year = Amount after 3 years - Amount after 2 years
⇒ Interest for 1 year = ₹3150 - ₹2700
⇒ Interest for 1 year = ₹450
Step 2: Calculate the total interest for 2 years.
Total interest for 2 years = 2 × ₹450
⇒ Total interest for 2 years = ₹900
Step 3: Calculate the principal amount.
Principal = Amount after 2 years - Total interest for 2 years
⇒ Principal = ₹2700 - ₹900
⇒ Principal = ₹1800
Step 4: Calculate the rate of interest per annum using the simple interest formula.
Simple Interest = Principal × Rate × Time / 100
⇒ ₹450 = ₹1800 × R × 1 / 100
⇒ ₹450 = ₹18R
⇒ R = ₹450 / ₹18
⇒ R = 25%
Therefore, the rate of interest per annum is 25%.