The difference between compound interest and simple interest on ₹ 20,000 for…
2019
The difference between compound interest and simple interest on ₹ 20,000 for two years at x% per annum is ₹ 512. What is the value of x?
- A.
16%
- B.
10%
- C.
14%
- D.
12%
Attempted by 39 students.
Show answer & explanation
Correct answer: A
Let P = ₹20,000, T = 2 years, and rate = x% per annum.
Key formula: Difference between compound interest and simple interest for 2 years = P × (R/100)².
Derivation (brief): CI for 2 years = P[(1 + R/100)² − 1] = P[2R/100 + (R/100)²]. SI for 2 years = 2PR/100. Subtracting gives P × (R/100)².
Set up the equation using the given difference: P × (x/100)² = 512.
Substitute P = 20000: 20000 × (x/100)² = 512 ⇒ (x/100)² = 512/20000 = 0.0256.
Take square root: x/100 = √0.0256 = 0.16.
Therefore x = 0.16 × 100 = 16.
Answer: x = 16% per annum
Quick check: 20000 × (0.16)² = 20000 × 0.0256 = ₹512, which matches the given difference.