the interest earned on rs.15000 in 3 years at simple interest is rs.5400. find the rate of interest per annum
The interest earned on Rs. 15,000 in 3 years at simple interest is Rs. 5,400. Find the rate of interest per annum.
Answer:
To solve this problem, we need to use the formula for calculating simple interest and then find the rate of interest.
Step 1: Understand the Simple Interest Formula
Simple interest (SI) can be calculated using the formula:
SI = \frac{P \times R \times T}{100}
Where:
- (SI) is the simple interest.
- (P) is the principal amount (initial amount of money).
- (R) is the rate of interest per annum.
- (T) is the time period in years.
Step 2: Identify the Known Values
From the problem, we know:
- (SI = 5,400) rupees
- (P = 15,000) rupees
- (T = 3) years
We need to find the rate of interest (R).
Step 3: Rearrange the Formula to Solve for Rate of Interest
We need to isolate (R) in the formula. Rearranging the simple interest formula gives:
R = \frac{SI \times 100}{P \times T}
Step 4: Plug in the Known Values
Now, substitute the known values into the rearranged formula:
R = \frac{5,400 \times 100}{15,000 \times 3}
Step 5: Perform the Calculations
- Calculate the numerator: (5,400 \times 100 = 540,000).
- Calculate the denominator: (15,000 \times 3 = 45,000).
- Divide the numerator by the denominator to find (R):
R = \frac{540,000}{45,000} = 12
Final Answer:
The rate of interest per annum is 12%.
By following these steps, anyone can use the basic formula for simple interest to find the rate when given the principal amount, time, and interest earned.