Shortcut Trick
Effective rate for Annual Compounding (10% for 2 years) = 10 + 10 + (10 × 10)/100 = 21%.
Effective rate for Semi-annual Compounding (5% for 4 periods) = 10.25 + 10.25 + (10.25 × 10.25)/100 = 21.550625%.
Difference in interest rates = 21.550625% − 21% = 0.550625%.
Savings = 0.550625% of ₹2,20,000 = (0.550625/100) × 2,20,000 = ₹1,211.375.
Rounding to one decimal place, the savings would be ₹1,211.40.
∴ The correct answer is ₹1211.40.
Alternate Method
Given:
Principal (P) = ₹2,20,000
Annual Rate (R) = 10%
Time (T) = 2 years
Formula Used: Amount (A) = P(1 + r/100)n
Step 1: Interest Compounded Annually
⇒ Amount1 = 2,20,000 × (1 + 10/100)2
⇒ Amount1 = 2,20,000 × (1.1) × (1.1) = 2,20,000 × 1.21 = ₹2,66,200
Step 2: Interest Compounded Semi-annually
⇒ Rate for 6 months = 10%/2 = 5%
⇒ Number of periods (n) = 2 × 2 = 4
⇒ Amount2 = 2,20,000 × (1 + 5/100)4
⇒ Amount2 = 2,20,000 × (1.05)4 = 2,20,000 × 1.21550625 = ₹2,67,411.375
Step 3: Difference (Savings)
⇒ Savings = Amount2 − Amount1
⇒ Savings = 2,67,411.375 − 2,66,200 = ₹1,211.375
⇒ Rounded to one decimal place = ₹1,211.40
∴ The correct answer is ₹1211.40.
Additional Information
Effective Rate of Interest
When interest is compounded k times a year at an annual rate r, the effective annual rate is (1 + r/k)k − 1.
Compound Interest vs. Simple Interest
For the first year, CI and SI are equal if compounded annually. From the second year onwards, CI > SI because interest is calculated on the accumulated amount.
Difference for 2 Years (SI & CI)
The difference between CI and SI for 2 years is given by the formula P(R/100)2.
Compounding Frequency
As the frequency of compounding increases (e.g., quarterly, monthly, daily), the total interest earned or charged also increases.