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Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.
- a)Rs. 5324
- b)Rs. 6934
- c)Rs. 7986
- d)Rs. 8986
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Raghav has to repay a loan of Rs. 12,820 in three annual instalments. ...
To find the value of the third installment that Raghav has to pay, we need to first determine the values of the first and second installments. Let's solve the problem step by step:
Given:
Total loan amount = Rs. 12,820
Rate of interest = 10%
Let the second installment be x. Then, the first installment will be half of x, i.e., 0.5x, and the third installment will be one-third of x, i.e., (1/3)x.
We know that Compound Interest (CI) formula is given by:
CI = P(1 + r/n)^(nt) - P
Where:
P is the principal amount
r is the rate of interest
n is the number of times the interest is compounded per year
t is the time in years
In this case, the principal amount for each installment is as follows:
First installment = Rs. 0.5x
Second installment = x
Third installment = (1/3)x
Now, let's calculate the compound interest for each installment:
First Installment:
Principal (P1) = Rs. 0.5x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI1 = P1(1 + r/n)^(nt) - P1
= 0.5x(1 + 0.1/1)^(1*1) - 0.5x
= 0.5x(1.1) - 0.5x
= 0.05x
Second Installment:
Principal (P2) = x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI2 = P2(1 + r/n)^(nt) - P2
= x(1 + 0.1/1)^(1*1) - x
= 1.1x - x
= 0.1x
Third Installment:
Principal (P3) = (1/3)x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI3 = P3(1 + r/n)^(nt) - P3
= (1/3)x(1 + 0.1/1)^(1*1) - (1/3)x
= (1/3)x(1.1) - (1/3)x
= 0.1x/3
Now, the total loan amount is the sum of the three installments:
Rs. 12,820 = 0.5x + x + 0.1x/3
To solve this equation, let's simplify it:
12,820 = (3/6)x + (6/6)x + (0.1/3)x
12,820 = (9/6)x + (0.1/3)x
12,820 = (18/6)x + (0.1/3)x
12,820 =
Given:
Total loan amount = Rs. 12,820
Rate of interest = 10%
Let the second installment be x. Then, the first installment will be half of x, i.e., 0.5x, and the third installment will be one-third of x, i.e., (1/3)x.
We know that Compound Interest (CI) formula is given by:
CI = P(1 + r/n)^(nt) - P
Where:
P is the principal amount
r is the rate of interest
n is the number of times the interest is compounded per year
t is the time in years
In this case, the principal amount for each installment is as follows:
First installment = Rs. 0.5x
Second installment = x
Third installment = (1/3)x
Now, let's calculate the compound interest for each installment:
First Installment:
Principal (P1) = Rs. 0.5x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI1 = P1(1 + r/n)^(nt) - P1
= 0.5x(1 + 0.1/1)^(1*1) - 0.5x
= 0.5x(1.1) - 0.5x
= 0.05x
Second Installment:
Principal (P2) = x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI2 = P2(1 + r/n)^(nt) - P2
= x(1 + 0.1/1)^(1*1) - x
= 1.1x - x
= 0.1x
Third Installment:
Principal (P3) = (1/3)x
Rate of interest (r) = 10% = 0.1
Number of times compounded per year (n) = 1
Time (t) = 1 year
CI3 = P3(1 + r/n)^(nt) - P3
= (1/3)x(1 + 0.1/1)^(1*1) - (1/3)x
= (1/3)x(1.1) - (1/3)x
= 0.1x/3
Now, the total loan amount is the sum of the three installments:
Rs. 12,820 = 0.5x + x + 0.1x/3
To solve this equation, let's simplify it:
12,820 = (3/6)x + (6/6)x + (0.1/3)x
12,820 = (9/6)x + (0.1/3)x
12,820 = (18/6)x + (0.1/3)x
12,820 =
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Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.a)Rs. 5324b)Rs. 6934c)Rs. 7986d)Rs. 8986e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.a)Rs. 5324b)Rs. 6934c)Rs. 7986d)Rs. 8986e)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.a)Rs. 5324b)Rs. 6934c)Rs. 7986d)Rs. 8986e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Raghav has to repay a loan of Rs. 12,820 in three annual instalments. The first instalment is to be half of the second and one-third of the third. If the compound interest is calculated annually at a rate of 10%, then find the value of the third instalment that Raghav has to pay.a)Rs. 5324b)Rs. 6934c)Rs. 7986d)Rs. 8986e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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