Shortcut Trick
For 3 years, the difference (D) between CI and SI is: D = P × (R/100)2 × (3 + R/100)
⇒ 61.60 = P × (8/100)2 × (3 + 8/100)
⇒ 61.60 = P × (64 / 10,000) × (308 / 100)
⇒ P = (61.60 × 1,000,000) ÷ (64 × 308) = 61,600,000 ÷ 19,712
⇒ P = ₹3,125
∴ The correct answer is ₹3,125.
Alternate Method
Given:
Rate (R) = 8% per annum | Time (T) = 3 years | Difference (D) = ₹61.60
Formula Used:
Difference for 3 years = PR2(300 + R) ÷ 1003
Calculations:
⇒ Let Principal = P
⇒ R = 8% = 2/25 (as a fraction)
⇒ Let P = 253 = 15,625 units
⇒ Simple Interest (SI) for 1 year = 15,625 × (2/25) = 1,250 units
⇒ SI for 3 years = 1,250 × 3 = 3,750 units
⇒ Compound Interest (CI) for 3 years = 15,625 × [(1 + 2/25)3 − 1]
⇒ CI = 15,625 × [(27/25)3 − 1] = 15,625 × [19,683/15,625 − 1]
⇒ CI = 19,683 − 15,625 = 4,058 units
⇒ Difference = 4,058 − 3,750 = 308 units
⇒ Given: 308 units = ₹61.60
⇒ 1 unit = 61.60 ÷ 308 = ₹0.2
⇒ Principal = 15,625 × 0.2 = ₹3,125
∴ The correct answer is ₹3,125.
Additional Information
Difference for 2 Years
The difference between CI and SI for 2 years is D = P(R/100)2.
Compound Interest Formula
The amount under CI is A = P(1 + R/100)T and CI = A − P.
Effective Rate Method
For 8% for 3 years, effective SI is 24% and effective CI is 25.9712%, making the difference 1.9712% of Principal.