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If the compound interest received on a certain amount in the 2nd year is Rs. 250. What will be the compound interest (in Rs.) for the 3rd year on the same amount at 12% rate of interest?
- a)250
- b)300
- c)280
- d)270
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the compound interest received on a certain amount in the 2nd year ...
CI of the 2nd year = Rs. 250
⇒ CI of the 3rd year will be = [CI of 2nd year] + [12% interest on CI of 2nd year].
∴ CI of 3rd year = 250 + 250 × 0.12 = Rs. 280
Most Upvoted Answer
If the compound interest received on a certain amount in the 2nd year ...
Given:
Compound interest received in the 2nd year = Rs. 250
Rate of interest = 12%
To find:
Compound interest for the 3rd year on the same amount
Solution:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the total amount after interest
P is the principal amount
r is the rate of interest
n is the number of times interest is compounded per year
t is the number of years
In this case, we know the principal amount, rate of interest, and the compound interest received in the 2nd year. We need to find the compound interest for the 3rd year.
Let's assume the principal amount is P.
Step 1:
We know that the compound interest for the 2nd year is Rs. 250.
Using the formula for compound interest, we can calculate the total amount after 2 years:
A = P(1 + r/100)^2
A = P(1 + 12/100)^2
A = P(1 + 0.12)^2
A = P(1.12)^2
The compound interest for the 2nd year is given as Rs. 250, so we can write the equation as:
A - P = 250
Substituting the value of A from the above equation:
P(1.12)^2 - P = 250
P(1.2544) - P = 250
0.2544P = 250
P = 250/0.2544
P ≈ 982.36 (rounded to 2 decimal places)
Therefore, the principal amount is approximately Rs. 982.36.
Step 2:
Now that we have the principal amount, we can calculate the compound interest for the 3rd year using the same formula:
A = P(1 + r/100)^3
A = 982.36(1 + 12/100)^3
A = 982.36(1 + 0.12)^3
A = 982.36(1.12)^3
The compound interest for the 3rd year is the difference between the total amount after 3 years and the principal amount:
Compound interest for the 3rd year = A - P
Compound interest for the 3rd year = 982.36(1.12)^3 - 982.36
Calculating this value:
Compound interest for the 3rd year ≈ 982.36(1.404928) - 982.36
Compound interest for the 3rd year ≈ 1380.09 - 982.36
Compound interest for the 3rd year ≈ 397.73
Therefore, the compound interest for the 3rd year on the same amount at a 12% rate of interest is approximately Rs. 397.73.
Summary:
The compound interest for the 3rd year on the same amount at a 12% rate of interest is approximately Rs. 397.73.
Compound interest received in the 2nd year = Rs. 250
Rate of interest = 12%
To find:
Compound interest for the 3rd year on the same amount
Solution:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the total amount after interest
P is the principal amount
r is the rate of interest
n is the number of times interest is compounded per year
t is the number of years
In this case, we know the principal amount, rate of interest, and the compound interest received in the 2nd year. We need to find the compound interest for the 3rd year.
Let's assume the principal amount is P.
Step 1:
We know that the compound interest for the 2nd year is Rs. 250.
Using the formula for compound interest, we can calculate the total amount after 2 years:
A = P(1 + r/100)^2
A = P(1 + 12/100)^2
A = P(1 + 0.12)^2
A = P(1.12)^2
The compound interest for the 2nd year is given as Rs. 250, so we can write the equation as:
A - P = 250
Substituting the value of A from the above equation:
P(1.12)^2 - P = 250
P(1.2544) - P = 250
0.2544P = 250
P = 250/0.2544
P ≈ 982.36 (rounded to 2 decimal places)
Therefore, the principal amount is approximately Rs. 982.36.
Step 2:
Now that we have the principal amount, we can calculate the compound interest for the 3rd year using the same formula:
A = P(1 + r/100)^3
A = 982.36(1 + 12/100)^3
A = 982.36(1 + 0.12)^3
A = 982.36(1.12)^3
The compound interest for the 3rd year is the difference between the total amount after 3 years and the principal amount:
Compound interest for the 3rd year = A - P
Compound interest for the 3rd year = 982.36(1.12)^3 - 982.36
Calculating this value:
Compound interest for the 3rd year ≈ 982.36(1.404928) - 982.36
Compound interest for the 3rd year ≈ 1380.09 - 982.36
Compound interest for the 3rd year ≈ 397.73
Therefore, the compound interest for the 3rd year on the same amount at a 12% rate of interest is approximately Rs. 397.73.
Summary:
The compound interest for the 3rd year on the same amount at a 12% rate of interest is approximately Rs. 397.73.
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If the compound interest received on a certain amount in the 2nd year is Rs. 250. What will be the compound interest (in Rs.) for the 3rd year on the same amount at 12% rate of interest?a)250b)300c)280d)270Correct answer is option 'C'. Can you explain this answer?
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