Shortcut Trick
For half-yearly compounding, Rate = 10% ÷ 2 = 5% and Time = 2 × 2 = 4 periods.
Effective rate for 4 periods at 5% = 21.550625%.
CI = 10,000 × 21.550625% = ₹2,155.0625.
∴ The correct answer is ₹2,155.0625.
Alternate Method
Given: Principal (P) = ₹10,000, Rate (R) = 10% p.a., Time (n) = 2 years.
Formula Used: Amount (A) = P(1 + r/100)t; CI = A − P.
⇒ For compounded half-yearly:
⇒ New Rate (r) = 10% ÷ 2 = 5% per half-year.
⇒ New Time (t) = 2 × 2 = 4 half-years.
⇒ A = 10,000 × (1 + 5/100)4
⇒ A = 10,000 × (21/20)4
⇒ A = 10,000 × (194481 / 160000)
⇒ A = 194481 ÷ 16 = ₹12,155.0625
⇒ CI = A − P = 12,155.0625 − 10,000
⇒ CI = ₹2,155.0625
∴ The correct answer is ₹2,155.0625.
Additional Information
Compounding Frequency
If compounded quarterly, divide rate by 4 and multiply time by 4. If compounded monthly, divide rate by 12 and multiply time by 12.
Effective Rate Formula
For two successive cycles of r%, effective rate = (r + r + r2/100)%.
CI vs SI Difference
Difference for 2 years = P(R/100)2. Difference for 3 years = P(R/100)2 × (3 + R/100).