The compound interest on a certain sum at a rate of 12% per annum for 2 years is ₹ 1,590. The simple interest on the same sum for double the time period and at half the interest rate per annum is:

Explanation

Given: The compound interest on a certain sum at a rate of 12% per annum for 2 years is ₹ 1,590. Concept used: C.I = P[(1 + R/100) T- 1] S.I = (P × T × R)/100 Here, P = Sum T = Time R = Rate Calculation: Let the sum be P According to the question, 1590 = P[(1 + 12/100) 2- 1] ⇒ 1590 = P[(1 + 3/25) 2 - 1] ⇒ 1590 = P[(28/25) 2 - 1] ⇒ 1590 = P[(784/625) - 1] ⇒ 1590 = P[(784 - 625)/625 ] ⇒ 1590 = P[159/625 ] ⇒ 6250 = P So, sum = ₹6250 Now, S.I = (6250 × 4 × 6)/100 ⇒ 1500 ∴ Required simple interest is ₹ 1,500.