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.
Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
A sum amounts to Rs. 18,600 after 3 years and to Rs. 27,900 after 6 years, at a certain rate percent p.a., when the interest is compounded annually. The sum is:
