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The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50?
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The compound interest on a sum for two years is Rs. 1,575 and the corr...
Solution:
Given,
Compound interest for 2 years = Rs. 1,575
Simple interest for 2 years = Rs. 1,500
Let the sum be P and rate of interest be R%.
Calculation of Compound Interest:
Using the formula for compound interest, we have:
P(1 + R/100)^2 - P = 1575
Simplifying the above equation, we get:
P(R/100)^2 + 2PR/100 - 1575 = 0
On solving the above quadratic equation, we get:
R = 5% or R = -32%
Since the rate of interest cannot be negative, we take R = 5%.
So, the sum is:
P = 1575/(1 + 5/100)^2 = Rs. 1,400
Calculation of Simple Interest:
Using the formula for simple interest, we have:
SI = P*R*2/100 = 1,400*5*2/100 = Rs. 140
Given simple interest for 2 years = Rs. 1,500
So, simple interest for 1 year = 750
Hence, the sum is:
P = 750/5 = Rs. 150
This is not possible as the sum cannot be less than the interest earned.
Therefore, the rate of interest cannot be 5%.
Calculation of Compound Interest for 3 Years:
Let the compound interest for 3 years be C.
Using the formula for compound interest, we have:
P(1 + R/100)^3 - P = C
Substituting the value of P as Rs. 1,400 and R as 32%, we get:
C = 1400(1 + 32/100)^3 - 1400 = Rs. 2,482.50
Hence, the compound interest on the same sum at the same rate of interest at the end of the third year is Rs. 2,482.50.
Therefore, the correct option is (b) Rs. 2,482.50.
Given,
Compound interest for 2 years = Rs. 1,575
Simple interest for 2 years = Rs. 1,500
Let the sum be P and rate of interest be R%.
Calculation of Compound Interest:
Using the formula for compound interest, we have:
P(1 + R/100)^2 - P = 1575
Simplifying the above equation, we get:
P(R/100)^2 + 2PR/100 - 1575 = 0
On solving the above quadratic equation, we get:
R = 5% or R = -32%
Since the rate of interest cannot be negative, we take R = 5%.
So, the sum is:
P = 1575/(1 + 5/100)^2 = Rs. 1,400
Calculation of Simple Interest:
Using the formula for simple interest, we have:
SI = P*R*2/100 = 1,400*5*2/100 = Rs. 140
Given simple interest for 2 years = Rs. 1,500
So, simple interest for 1 year = 750
Hence, the sum is:
P = 750/5 = Rs. 150
This is not possible as the sum cannot be less than the interest earned.
Therefore, the rate of interest cannot be 5%.
Calculation of Compound Interest for 3 Years:
Let the compound interest for 3 years be C.
Using the formula for compound interest, we have:
P(1 + R/100)^3 - P = C
Substituting the value of P as Rs. 1,400 and R as 32%, we get:
C = 1400(1 + 32/100)^3 - 1400 = Rs. 2,482.50
Hence, the compound interest on the same sum at the same rate of interest at the end of the third year is Rs. 2,482.50.
Therefore, the correct option is (b) Rs. 2,482.50.
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The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50?
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The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50?.
The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a sum for two years is Rs. 1,575 and the corresponding simple interest is Rs. 1,500. Find the compound interest on the same sum at the same rate of interest at the end of third year. (b)Rs. 2,482.50 (a)Rs. 2,428.50 (d)Rs. 2,382.50 (c)Rs. 2,284.50?.
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