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The C.I on Rs. 4000 for 6 months at 12% p.a. payable quarterly is
- a)Rs. 243.60
- b)Rs. 240
- c)Rs. 243
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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The C.I on Rs. 4000 for 6 months at 12% p.a. payable quarterly isa)Rs....
Given:
Principal amount (P) = Rs. 4000
Rate of interest (R) = 12% per annum
Time period (T) = 6 months
Interest is payable quarterly
We need to find the compound interest (CI) on the given amount.
First, we need to calculate the interest for each quarter:
Interest for the first quarter = (P * R * 1/4) / 100 = (4000 * 12 * 1/4) / 100 = Rs. 120
Interest for the second quarter = (P + Interest for the first quarter) * R * 1/4 / 100 = (4120 * 12 * 1/4) / 100 = Rs. 123.60
Interest for the third quarter = (P + Interest for the second quarter) * R * 1/4 / 100 = (4243.60 * 12 * 1/4) / 100 = Rs. 127.01
Interest for the fourth quarter = (P + Interest for the third quarter) * R * 1/4 / 100 = (4370.61 * 12 * 1/4) / 100 = Rs. 130.42
Now, we can calculate the total compound interest (CI) for 6 months by adding the interest for all four quarters:
CI = P * (1 + R/100)^n - P
where n = number of compounding periods in the given time period = 4
CI = 4000 * (1 + 12/100/4)^4 - 4000 = Rs. 243.60
Therefore, the compound interest (CI) on Rs. 4000 for 6 months at 12% p.a. payable quarterly is Rs. 243.60 (Option A).
Principal amount (P) = Rs. 4000
Rate of interest (R) = 12% per annum
Time period (T) = 6 months
Interest is payable quarterly
We need to find the compound interest (CI) on the given amount.
First, we need to calculate the interest for each quarter:
Interest for the first quarter = (P * R * 1/4) / 100 = (4000 * 12 * 1/4) / 100 = Rs. 120
Interest for the second quarter = (P + Interest for the first quarter) * R * 1/4 / 100 = (4120 * 12 * 1/4) / 100 = Rs. 123.60
Interest for the third quarter = (P + Interest for the second quarter) * R * 1/4 / 100 = (4243.60 * 12 * 1/4) / 100 = Rs. 127.01
Interest for the fourth quarter = (P + Interest for the third quarter) * R * 1/4 / 100 = (4370.61 * 12 * 1/4) / 100 = Rs. 130.42
Now, we can calculate the total compound interest (CI) for 6 months by adding the interest for all four quarters:
CI = P * (1 + R/100)^n - P
where n = number of compounding periods in the given time period = 4
CI = 4000 * (1 + 12/100/4)^4 - 4000 = Rs. 243.60
Therefore, the compound interest (CI) on Rs. 4000 for 6 months at 12% p.a. payable quarterly is Rs. 243.60 (Option A).
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Community Answer
The C.I on Rs. 4000 for 6 months at 12% p.a. payable quarterly isa)Rs....
P = 4000
As the interest is payable quarterly,
i = I/400 = 12/400=0.03
n = 4N = 4× 6/12 = 2
CI = P[(1+i)^n - 1]
= 4000 [(1+0.03)² -1]
= 4000 [(1.03)² - 1]
=4000 [1.0609 - 1]
= 4000(0.0609)
= 243.60
As the interest is payable quarterly,
i = I/400 = 12/400=0.03
n = 4N = 4× 6/12 = 2
CI = P[(1+i)^n - 1]
= 4000 [(1+0.03)² -1]
= 4000 [(1.03)² - 1]
=4000 [1.0609 - 1]
= 4000(0.0609)
= 243.60
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