The difference between the compound and simple interest on a certain sum ofr 2…
2023
The difference between the compound and simple interest on a certain sum ofr 2 years at the rate of 8% per annum is Rs 80 . What is the sum ?
- A.
11,880
- B.
12,500
- C.
13,500
- D.
14,270
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Answer: Rs 12,500
Key idea: For 2 years, the difference between compound interest (annual compounding) and simple interest equals P * R^2 / 10000.
Step 1: Write the relation for the difference for 2 years: Difference = P * R^2 / 10000.
Step 2: Substitute Difference = 80 and R = 8: 80 = P * 8^2 / 10000 = P * 64 / 10000.
Step 3: Solve for P: P = 80 * 10000 / 64 = 80 * 156.25 = 12,500.
Note: The compact expression Sum = Difference * (100/R)^n shown earlier is not a generally valid formula for all n. The simplified relation used here (Difference = P * R^2 / 10000) is specific to n = 2 and is the correct basis for this question.