Shortcut Trick
Half-yearly rate = 20% ÷ 2 = 10% (1/10) and Time = 2.5 × 2 = 5 cycles.
For 5 cycles, P = 105 = 100000 units, A = 115 = 161051 units.
Compound Interest (CI) = 161051 − 100000 = 61051 units.
Since P = 100000 units = Rs. 3,00,000, Total CI = 61051 × 3 = Rs. 1,83,153.
∴ The correct answer is Rs. 1,83,153.
Alternate Method
Given:
⇒ Principal (P) = Rs. 3,00,000
⇒ Rate of interest (R) = 20% per annum
⇒ Time (T) = 2.5 years
Formula Used:
⇒ A = P(1 + R/100)n
Calculations:
⇒ Since interest is compounded half-yearly, Rate = 20% ÷ 2 = 10%
⇒ Number of conversion periods (n) = 2.5 × 2 = 5
⇒ A = 3,00,000 × (1 + 10/100)5
⇒ A = 3,00,000 × (11/10)5
⇒ A = 3,00,000 × (161051 / 100000)
⇒ A = 3 × 161051 = 4,83,153
⇒ Compound Interest (CI) = A − P
⇒ CI = 4,83,153 − 3,00,000 = 1,83,153
∴ The correct answer is Rs. 1,83,153.
Additional Information
Half-yearly Compounding
When interest is compounded half-yearly, the given annual rate is divided by 2, and the total time period in years is multiplied by 2.
Quarterly Compounding
When interest is compounded quarterly, the given annual rate is divided by 4, and the time period is multiplied by 4.
Successive Multiplication Factor
Amount can be directly calculated using successive multiplying factors based on rate fractions. For a 10% rate, the multiplying factor is 11/10 per cycle.