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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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Most Upvoted Answer
A certain amount of money earns Rs. 540 as simple interest in 3 years....
Given data:
Simple Interest (SI) = Rs. 540, Time (T) = 3 years, Compound Interest (CI) = Rs. 376.20, Time (T) = 2 years
Let the principal amount be P and the rate of interest be R% per annum.
Formula:
Simple Interest = (P x R x T)/100
Compound Interest = P[(1+R/100)^T - 1]
Calculation:
From the given data, we have:
540 = (P x R x 3)/100 ---(1)
376.20 = P[(1+R/100)^2 - 1] ---(2)
Solving equations (1) and (2) for P, we get:
P = 18000/R ---(3)
Substituting equation (3) in equation (2), we get:
376.20 = (18000/R)[(1+R/100)^2 - 1]
376.20R = 18000[(1+R/100)^2 - 1]
376.20R = 18000(1+2R/100+R^2/10000 - 1)
376.20R = 360R + 18R^2
18R^2 + 16.6R - 376.20 = 0
9R^2 + 8.3R - 188.10 = 0
Using the quadratic formula, we get:
R = (-8.3 + sqrt(8.3^2 + 4 x 9 x 188.10))/(2 x 9) or R = (-8.3 - sqrt(8.3^2 + 4 x 9 x 188.10))/(2 x 9)
R = 10% or R = -21.1111% (which is not possible)
Hence, the rate of interest is 10% per annum.
Substituting R = 10 in equation (1), we get:
540 = (P x 10 x 3)/100
P = Rs. 1800
Therefore, the principal amount is Rs. 1800.
Simple Interest (SI) = Rs. 540, Time (T) = 3 years, Compound Interest (CI) = Rs. 376.20, Time (T) = 2 years
Let the principal amount be P and the rate of interest be R% per annum.
Formula:
Simple Interest = (P x R x T)/100
Compound Interest = P[(1+R/100)^T - 1]
Calculation:
From the given data, we have:
540 = (P x R x 3)/100 ---(1)
376.20 = P[(1+R/100)^2 - 1] ---(2)
Solving equations (1) and (2) for P, we get:
P = 18000/R ---(3)
Substituting equation (3) in equation (2), we get:
376.20 = (18000/R)[(1+R/100)^2 - 1]
376.20R = 18000[(1+R/100)^2 - 1]
376.20R = 18000(1+2R/100+R^2/10000 - 1)
376.20R = 360R + 18R^2
18R^2 + 16.6R - 376.20 = 0
9R^2 + 8.3R - 188.10 = 0
Using the quadratic formula, we get:
R = (-8.3 + sqrt(8.3^2 + 4 x 9 x 188.10))/(2 x 9) or R = (-8.3 - sqrt(8.3^2 + 4 x 9 x 188.10))/(2 x 9)
R = 10% or R = -21.1111% (which is not possible)
Hence, the rate of interest is 10% per annum.
Substituting R = 10 in equation (1), we get:
540 = (P x 10 x 3)/100
P = Rs. 1800
Therefore, the principal amount is Rs. 1800.
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Community Answer
A certain amount of money earns Rs. 540 as simple interest in 3 years....
1 year S.I. = 540÷3=180
2(CI-SI) = 376.20-360=16.20
rate= 16.20÷180×100=9%
=> X×9%=180=> X=2000
Amount(2 years) = 2000+376.20
2(CI-SI) = 376.20-360=16.20
rate= 16.20÷180×100=9%
=> X×9%=180=> X=2000
Amount(2 years) = 2000+376.20
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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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