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What is the C.I. on Rs. 8000 for 1 year at 5% p.a. payable half-yearly?
- a)Rs. 800
- b)Rs. 810
- c)Rs. 400
- d)Rs. 405
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the C.I. on Rs. 8000 for 1 year at 5% p.a. payable half-yearly...
A = P ( 1 + R/100)t. Since its half yearly,
t = 2
= 8000 (1 + 5/200)2
= 8405
CI = A-P = 8405 - 8000 = 405
t = 2
= 8000 (1 + 5/200)2
= 8405
CI = A-P = 8405 - 8000 = 405
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What is the C.I. on Rs. 8000 for 1 year at 5% p.a. payable half-yearly...
Interest Calculation
To find the compound interest (CI) on Rs. 8000 for 1 year at 5% p.a. payable half-yearly, we need to calculate the interest earned at each half-yearly interval and add it to the principal amount.
Step 1: Calculate the interest for the first half-yearly period.
Principal amount (P) = Rs. 8000
Rate of interest (R) = 5% = 0.05
Time period (T) = 1 year = 2 half-yearly periods
Using the formula for compound interest: CI = P(1 + R/n)^(n*T) - P
where n is the number of compounding periods per year,
CI1 = 8000(1 + 0.05/2)^(2*1) - 8000
= 8000(1.025)^2 - 8000
= 8000(1.050625) - 8000
= 8405 - 8000
= Rs. 405
Step 2: Calculate the interest for the second half-yearly period.
Principal amount (P) = Rs. 8405 (including the interest from the first half-yearly period)
Rate of interest (R) = 5% = 0.05
Time period (T) = 1 year = 2 half-yearly periods
CI2 = 8405(1 + 0.05/2)^(2*1) - 8405
= 8405(1.025)^2 - 8405
= 8405(1.050625) - 8405
= Rs. 440.31
Step 3: Total compound interest for 1 year = CI1 + CI2
CI_total = 405 + 440.31
= Rs. 845.31
Therefore, the compound interest on Rs. 8000 for 1 year at 5% p.a. payable half-yearly is Rs. 845.31.
Answer: d) Rs. 405
To find the compound interest (CI) on Rs. 8000 for 1 year at 5% p.a. payable half-yearly, we need to calculate the interest earned at each half-yearly interval and add it to the principal amount.
Step 1: Calculate the interest for the first half-yearly period.
Principal amount (P) = Rs. 8000
Rate of interest (R) = 5% = 0.05
Time period (T) = 1 year = 2 half-yearly periods
Using the formula for compound interest: CI = P(1 + R/n)^(n*T) - P
where n is the number of compounding periods per year,
CI1 = 8000(1 + 0.05/2)^(2*1) - 8000
= 8000(1.025)^2 - 8000
= 8000(1.050625) - 8000
= 8405 - 8000
= Rs. 405
Step 2: Calculate the interest for the second half-yearly period.
Principal amount (P) = Rs. 8405 (including the interest from the first half-yearly period)
Rate of interest (R) = 5% = 0.05
Time period (T) = 1 year = 2 half-yearly periods
CI2 = 8405(1 + 0.05/2)^(2*1) - 8405
= 8405(1.025)^2 - 8405
= 8405(1.050625) - 8405
= Rs. 440.31
Step 3: Total compound interest for 1 year = CI1 + CI2
CI_total = 405 + 440.31
= Rs. 845.31
Therefore, the compound interest on Rs. 8000 for 1 year at 5% p.a. payable half-yearly is Rs. 845.31.
Answer: d) Rs. 405
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