Correct Answer - Option 3 : Rs. 7785
Given:
The Simple Interest, SI = 5880
Time, n = 2.5 years
Rate of Interest, r = 10%
Time = 3 years for CI
Formula:
SI = PRT/100
Amount = P(1 + R/100)n
CI = P(1 + R/100)n - P
Calculations:
The principal, P, is calculated as:
SI = PRT/100
⇒ 5880 = (P × 10 × 2.5)/100
⇒ P = (5880 × 100)/25
⇒ 23520
∴ the Principal is Rs. 23520.
The compound interest for the same sum in 3 years is calculated as follows;
⇒ CI = Amount - Principal
⇒ Amount = P(1 + r/100)3
⇒ CI = P (1 + r/100)3 – P
⇒ 23520 (1 + 10/100)3 – 23520
⇒ 23520 (110/100)3 – 23520
⇒ (23520 × (11/10)3) – 23520
⇒ 31305.12 – 23520
⇒ Rs. 7785.12 = Rs. 7785
∴ compound interest is Rs. 7785