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What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?
- a)4%
- b)5%
- c)3%
- d)6%
Correct answer is option 'B'. Can you explain this answer?
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What is the rate of simple interest for the first 4 years if the sum o...
For the last 5 years, the interest earned would be: 30% of 360 = 108. Thus, interest earned in the first 4 years would be Rs. 72 → Rs. 18 every year on an amount of Rs. 360- which means that the rate of interest is 5%
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What is the rate of simple interest for the first 4 years if the sum o...
Given, principal amount (P) = Rs. 360, and it becomes Rs. 540 in 9 years.
Let the rate of interest for the first 4 years be R.
Using the simple interest formula,
Simple Interest (SI) = P*R*T/100
where T is the time in years.
For the first 4 years,
SI = 360*R*4/100 = 14.4R
The remaining 5 years have an interest rate of 6%.
Using the compound interest formula,
Amount (A) = P*(1 + R/100)^T
where T is the time in years.
For the remaining 5 years,
A = 360*(1 + 6/100)^5 = Rs. 478.30
Total amount after 9 years = Rs. 540
Therefore,
Total SI = 540 - 478.30 = Rs. 61.70
Total SI = SI for first 4 years + SI for next 5 years
61.70 = 14.4R + (360*6*5/100)
61.70 = 14.4R + 108
14.4R = -46.3
R = -3.215
Since the rate of interest cannot be negative,
R = 3.215 ≈ 3%
Hence, the rate of interest for the first 4 years is 3%.
Therefore, option (c) 3% is the correct answer.
Let the rate of interest for the first 4 years be R.
Using the simple interest formula,
Simple Interest (SI) = P*R*T/100
where T is the time in years.
For the first 4 years,
SI = 360*R*4/100 = 14.4R
The remaining 5 years have an interest rate of 6%.
Using the compound interest formula,
Amount (A) = P*(1 + R/100)^T
where T is the time in years.
For the remaining 5 years,
A = 360*(1 + 6/100)^5 = Rs. 478.30
Total amount after 9 years = Rs. 540
Therefore,
Total SI = 540 - 478.30 = Rs. 61.70
Total SI = SI for first 4 years + SI for next 5 years
61.70 = 14.4R + (360*6*5/100)
61.70 = 14.4R + 108
14.4R = -46.3
R = -3.215
Since the rate of interest cannot be negative,
R = 3.215 ≈ 3%
Hence, the rate of interest for the first 4 years is 3%.
Therefore, option (c) 3% is the correct answer.
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What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?a)4% b)5%c)3% d)6%Correct answer is option 'B'. Can you explain this answer?
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