A certain amount earns simple interest of Rs. 1250 after 5 years. Had ...
Given:
- The amount earns simple interest of Rs. 1250 after 5 years.
To find:
- How much more interest would it have earned if the interest per annum was 2% less.
Solution:
Step 1: Calculate the rate of interest
Let the principal amount be P and the rate of interest be R%.
Simple interest formula: SI = (P * R * T) / 100
Given that the simple interest is Rs. 1250 and the time period is 5 years, we can rewrite the formula as:
1250 = (P * R * 5) / 100
Simplifying the equation, we get:
25PR = 1250
Dividing both sides by 25:
PR = 50
Therefore, the rate of interest is 50/R%.
Step 2: Calculate the new interest
If the interest per annum is 2% less than the original rate, the new rate of interest will be (50 - 2) = 48/R%.
Using the new rate of interest, we can calculate the new interest earned.
New simple interest formula: new_SI = (P * (48/R) * 5) / 100
Step 3: Find the difference in interest
The difference in interest is given by:
Difference = new_SI - SI
Substituting the values, we get:
Difference = ((P * (48/R) * 5) / 100) - ((P * R * 5) / 100)
Difference = (P * 240/R - P * 5R) / 100
Difference = P * (240/R - 5R) / 100
Since we do not know the value of P, we cannot calculate the difference in interest. Hence, the answer is "Cannot be determined" (option D).