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For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is
Correct answer is '90000'. Can you explain this answer?
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For the same principal amount, the compound interest for two years at...
Given:
- Compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125.
To find:
The principal amount in rupees.
Approach:
Let's assume the principal amount is P.
We can calculate the compound interest using the formula:
Compound Interest = P(1 + r/100)^n - P
where r is the rate of interest and n is the number of years.
Similarly, we can calculate the simple interest using the formula:
Simple Interest = (P * r * n)/100
We are given that the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125.
So we can set up the equation:
P(1 + 5/100)^2 - P = (P * 3 * 3)/100 + 1125
Simplifying the equation:
P(1.05^2 - 1) = (9P)/100 + 1125
P(1.1025 - 1) = (9P)/100 + 1125
0.1025P = (9P)/100 + 1125
Now, let's solve this equation to find the value of P.
Solution:
0.1025P - (9P)/100 = 1125
0.1025P - 0.09P = 1125
0.0125P = 1125
P = 1125/0.0125
P = 90000
Therefore, the principal amount is Rs 90000.
- Compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125.
To find:
The principal amount in rupees.
Approach:
Let's assume the principal amount is P.
We can calculate the compound interest using the formula:
Compound Interest = P(1 + r/100)^n - P
where r is the rate of interest and n is the number of years.
Similarly, we can calculate the simple interest using the formula:
Simple Interest = (P * r * n)/100
We are given that the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125.
So we can set up the equation:
P(1 + 5/100)^2 - P = (P * 3 * 3)/100 + 1125
Simplifying the equation:
P(1.05^2 - 1) = (9P)/100 + 1125
P(1.1025 - 1) = (9P)/100 + 1125
0.1025P = (9P)/100 + 1125
Now, let's solve this equation to find the value of P.
Solution:
0.1025P - (9P)/100 = 1125
0.1025P - 0.09P = 1125
0.0125P = 1125
P = 1125/0.0125
P = 90000
Therefore, the principal amount is Rs 90000.
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Community Answer
For the same principal amount, the compound interest for two years at...
For two years the compound interest is
For three years the simple interest is
Now R(1)= 5% and R=3%
Solving we get P = 90000
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For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees isCorrect answer is '90000'. Can you explain this answer?
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