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A certain amount of money earns Rs. 540 as simple interest in 3 years. If it earns a compound interest of Rs. 376.20 at the same rate of interest in 2 years, find the amount (in Rupees).
- a)1600
- b)1800
- c)2100
- d)2000
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A certain amount of money earns Rs. 540 as simple interest in 3 years....
From (i) P× R = 18000
P × 9 = 18000
P = Rs. 2000
Most Upvoted Answer
A certain amount of money earns Rs. 540 as simple interest in 3 years....
From (i) P× R = 18000
P × 9 = 18000
P = Rs. 2000
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Community Answer
A certain amount of money earns Rs. 540 as simple interest in 3 years....
Given:
- Simple interest earned in 3 years = Rs. 540
- Compound interest earned in 2 years = Rs. 376.20
To find:
- The principal amount (in Rupees)
Solution:
To solve this problem, we need to understand the formulas for simple interest and compound interest.
1. Simple Interest Formula:
Simple Interest (SI) = (Principal * Rate * Time) / 100
2. Compound Interest Formula:
Compound Interest (CI) = Principal * {(1 + Rate/100)^Time - 1}
Now, let's solve the problem step by step.
Step 1:
Using the simple interest formula, we can calculate the rate of interest.
SI = (Principal * Rate * Time) / 100
540 = (Principal * Rate * 3) / 100
Rate = (540 * 100) / (Principal * 3)
Rate = 18000 / Principal
Step 2:
Using the compound interest formula, we can calculate the rate of interest.
CI = Principal * {(1 + Rate/100)^Time - 1}
376.20 = Principal * {(1 + (18000 / Principal) / 100)^2 - 1}
376.20 = Principal * {(1 + 180 / Principal)^2 - 1}
376.20 = Principal * {(Principal + 180)^2 - 1} / Principal^2
376.20 = (Principal + 180)^2 - 1
377.20 = (Principal + 180)^2
Step 3:
To find the value of Principal, we take the square root of both sides of the equation.
Principal + 180 = √377.20
Principal + 180 = 19.4
Principal = 19.4 - 180
Principal = -160.6
Since the principal amount cannot be negative, we discard this solution.
Therefore, the correct answer is D) 2000 Rupees.
- Simple interest earned in 3 years = Rs. 540
- Compound interest earned in 2 years = Rs. 376.20
To find:
- The principal amount (in Rupees)
Solution:
To solve this problem, we need to understand the formulas for simple interest and compound interest.
1. Simple Interest Formula:
Simple Interest (SI) = (Principal * Rate * Time) / 100
2. Compound Interest Formula:
Compound Interest (CI) = Principal * {(1 + Rate/100)^Time - 1}
Now, let's solve the problem step by step.
Step 1:
Using the simple interest formula, we can calculate the rate of interest.
SI = (Principal * Rate * Time) / 100
540 = (Principal * Rate * 3) / 100
Rate = (540 * 100) / (Principal * 3)
Rate = 18000 / Principal
Step 2:
Using the compound interest formula, we can calculate the rate of interest.
CI = Principal * {(1 + Rate/100)^Time - 1}
376.20 = Principal * {(1 + (18000 / Principal) / 100)^2 - 1}
376.20 = Principal * {(1 + 180 / Principal)^2 - 1}
376.20 = Principal * {(Principal + 180)^2 - 1} / Principal^2
376.20 = (Principal + 180)^2 - 1
377.20 = (Principal + 180)^2
Step 3:
To find the value of Principal, we take the square root of both sides of the equation.
Principal + 180 = √377.20
Principal + 180 = 19.4
Principal = 19.4 - 180
Principal = -160.6
Since the principal amount cannot be negative, we discard this solution.
Therefore, the correct answer is D) 2000 Rupees.
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A certain amount of money earns Rs. 540 as simple interest in 3 years. If it earns a compound interest of Rs. 376.20 at the same rate of interest in 2 years, find the amount (in Rupees).a)1600b)1800c)2100d)2000Correct answer is option 'D'. Can you explain this answer?
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