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A certain sum at a certain rate of compound interest per annum amounts to Rs. 36,000 in 4 years and Rs. 37,800 in 5 years. What is the rate of interest?
- a)4%
- b)5%
- c)6.25%
- d)8%
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A certain sum at a certain rate of compound interest per annum amounts...
In one year Rs. 36,000 becomes Rs. 37,800.
Hence, Option B is correct.
Hence, Option B is correct.
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Community Answer
A certain sum at a certain rate of compound interest per annum amounts...
Understanding the Problem
We have a sum that amounts to Rs. 36,000 in 4 years and Rs. 37,800 in 5 years under compound interest.
Finding the Interest Amount
The interest earned in the 5th year can be calculated as follows:
- Amount after 5 years: Rs. 37,800
- Amount after 4 years: Rs. 36,000
The interest earned in the 5th year is:
Interest in 5th Year = Amount after 5 years - Amount after 4 years
- Interest in 5th Year = Rs. 37,800 - Rs. 36,000 = Rs. 1,800
Relating Interest to Principal
In compound interest, the interest for any year is calculated on the amount at the end of the previous year. Therefore, we can express the interest earned in the 5th year as a percentage of the amount after 4 years:
Interest for 5th Year = Principal (Amount after 4 years) × Rate
- Rs. 1,800 = Rs. 36,000 × Rate
Calculating the Rate
Rearranging the equation to find the rate:
- Rate = Interest / Principal
- Rate = Rs. 1,800 / Rs. 36,000
Calculating the Rate Percentage
- Rate = 1,800 / 36,000 = 0.05
To express this as a percentage:
- Rate = 0.05 × 100 = 5%
Conclusion
The rate of interest is therefore:
Correct Answer: 5% (Option B)
We have a sum that amounts to Rs. 36,000 in 4 years and Rs. 37,800 in 5 years under compound interest.
Finding the Interest Amount
The interest earned in the 5th year can be calculated as follows:
- Amount after 5 years: Rs. 37,800
- Amount after 4 years: Rs. 36,000
The interest earned in the 5th year is:
Interest in 5th Year = Amount after 5 years - Amount after 4 years
- Interest in 5th Year = Rs. 37,800 - Rs. 36,000 = Rs. 1,800
Relating Interest to Principal
In compound interest, the interest for any year is calculated on the amount at the end of the previous year. Therefore, we can express the interest earned in the 5th year as a percentage of the amount after 4 years:
Interest for 5th Year = Principal (Amount after 4 years) × Rate
- Rs. 1,800 = Rs. 36,000 × Rate
Calculating the Rate
Rearranging the equation to find the rate:
- Rate = Interest / Principal
- Rate = Rs. 1,800 / Rs. 36,000
Calculating the Rate Percentage
- Rate = 1,800 / 36,000 = 0.05
To express this as a percentage:
- Rate = 0.05 × 100 = 5%
Conclusion
The rate of interest is therefore:
Correct Answer: 5% (Option B)
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