What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
80
Shortcut Trick
Compound interest rate% for 1 year when compounded annually = 8%
Compound interest rate% for 1 year when compounded half-yearly = [4 + 4 + (4 × 4)/100]%
⇒ 8.16%
Difference between rate percentages = 8.16% - 8% = 0.16%
Difference in interest = 0.16% of 50,000 = 80
∴ The required difference is Rs. 80.
Additional Information
Given:
Principal (P) = Rs. 50,000
Rate (r) = 8%
Formula Used:
A1 = P(1 + r)t
A2 = P(1 + r/2)2t
Calculation:
When interest is compounded annually,
A1 = P(1 + r)t
⇒ 50,000 × (1 + 8/100)1
⇒ (50,000 × 108/100)
⇒ Rs. 54,000
Now,
When interest is compounded half-yearly,
A2 = P(1 + r/2)2t
⇒ 50,000 × (1 + 8/200)2
⇒ (50,000 × 208/200 × 208/200)
⇒ (5 × 52 × 208) Rs.
⇒ Rs. 54,080
Now,
Difference between the interest compounded half-yearly and annually = Rs. (54,080 – 54,000)
⇒ Rs. 80
∴ The required difference is Rs. 80.
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