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The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350. What is definitely the rate of interest per cent per annum?
- a)9,300
- b)7600
- c)12000
- d)Data inadequate
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The difference between the total simple interest and the total compoun...
Difference = Pr2 /(100)2
= (350×100×100)/(P×r2)
P is not given
= (350×100×100)/(P×r2)
P is not given
Most Upvoted Answer
The difference between the total simple interest and the total compoun...
Given:
- The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350.
To find:
- The rate of interest per cent per annum.
Assumption:
- Let the principal amount be P.
Formula:
- Simple Interest (SI) = P * (rate/100) * time
- Compound Interest (CI) = P * (1 + rate/100)^time - P
Calculation:
Let's assume the rate of interest per annum is R%.
After two years, the total Simple Interest (SI) would be:
SI = P * (R/100) * 2
The total Compound Interest (CI) would be:
CI = P * (1 + R/100)^2 - P
According to the given condition, the difference between SI and CI is Rs. 350:
SI - CI = 350
Substituting the values of SI and CI:
P * (R/100) * 2 - [P * (1 + R/100)^2 - P] = 350
Simplifying the equation:
2PR/100 - [(1 + R/100)^2 - 1] * P = 350
2PR/100 - (1 + 2R/100 + R^2/10000 - 1) * P = 350
2PR/100 - (2R/100 + R^2/10000) * P = 350
2PR - 2RP - R^2P/100 = 35000
2PR - 2RP - R^2P = 35000 * 100
2PR - 2RP - R^2P = 3500000
Factoring out common terms:
P (2R - 2R - R^2) = 3500000
P (-R^2) = 3500000
R^2 = -3500000/P
Since the interest rate cannot be negative, it is not possible to determine the exact rate of interest per cent per annum. Therefore, the data provided is inadequate to determine the rate of interest. Hence, the correct answer is option D.
- The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350.
To find:
- The rate of interest per cent per annum.
Assumption:
- Let the principal amount be P.
Formula:
- Simple Interest (SI) = P * (rate/100) * time
- Compound Interest (CI) = P * (1 + rate/100)^time - P
Calculation:
Let's assume the rate of interest per annum is R%.
After two years, the total Simple Interest (SI) would be:
SI = P * (R/100) * 2
The total Compound Interest (CI) would be:
CI = P * (1 + R/100)^2 - P
According to the given condition, the difference between SI and CI is Rs. 350:
SI - CI = 350
Substituting the values of SI and CI:
P * (R/100) * 2 - [P * (1 + R/100)^2 - P] = 350
Simplifying the equation:
2PR/100 - [(1 + R/100)^2 - 1] * P = 350
2PR/100 - (1 + 2R/100 + R^2/10000 - 1) * P = 350
2PR/100 - (2R/100 + R^2/10000) * P = 350
2PR - 2RP - R^2P/100 = 35000
2PR - 2RP - R^2P = 35000 * 100
2PR - 2RP - R^2P = 3500000
Factoring out common terms:
P (2R - 2R - R^2) = 3500000
P (-R^2) = 3500000
R^2 = -3500000/P
Since the interest rate cannot be negative, it is not possible to determine the exact rate of interest per cent per annum. Therefore, the data provided is inadequate to determine the rate of interest. Hence, the correct answer is option D.
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Community Answer
The difference between the total simple interest and the total compoun...
Difference = Pr2 /(100)2
= (350×100×100)/(P×r2)
P is not given
= (350×100×100)/(P×r2)
P is not given
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