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A sum of Rs. 8400 was taken as loan. This is to be paid in two equal annual installments. If the rate of interest be 20% compounded annually, then the value of each installment is
- a)5400
- b)5700
- c)5100
- d)5200
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A sum of Rs. 8400 was taken as loan. This is to be paid in two equal a...
Let value of each installment be X.
X/(1 + 20/100) + X/(1 + 20/100)² = 8400
⇒ X(5/6 + 25/36) = 8400
⇒ X(56/36) = 8400
X = 5400
X/(1 + 20/100) + X/(1 + 20/100)² = 8400
⇒ X(5/6 + 25/36) = 8400
⇒ X(56/36) = 8400
X = 5400
Most Upvoted Answer
A sum of Rs. 8400 was taken as loan. This is to be paid in two equal a...
Let value of each installment be X.
X/(1 + 20/100) + X/(1 + 20/100)² = 8400
⇒ X(5/6 + 25/36) = 8400
⇒ X(56/36) = 8400
X = 5400
X/(1 + 20/100) + X/(1 + 20/100)² = 8400
⇒ X(5/6 + 25/36) = 8400
⇒ X(56/36) = 8400
X = 5400
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Community Answer
A sum of Rs. 8400 was taken as loan. This is to be paid in two equal a...
Given:
Principal amount (P) = Rs. 8400
Number of installments (n) = 2
Rate of interest (r) = 20% compounded annually
To find: Value of each installment
Formula used:
EMI formula = [P x r x (1 + r)^n] / [(1 + r)^n – 1]
Calculation:
As the loan is to be paid in two equal annual installments, the total amount to be paid will be the sum of two installments.
Total amount to be paid = 2 x Value of each installment
Let’s calculate the value of each installment using the EMI formula.
EMI formula = [P x r x (1 + r)^n] / [(1 + r)^n – 1]
= [8400 x 0.2 x (1 + 0.2)^2] / [(1 + 0.2)^2 – 1]
= (8400 x 0.2 x 1.44) / 0.44
= 6912 / 0.44
= Rs. 15709.09 (approx.)
Therefore, the total amount to be paid will be 2 x Rs. 15709.09 = Rs. 31418.18 (approx.)
And, the value of each installment will be Rs. 31418.18 / 2 = Rs. 15709.09 / 2 = Rs. 7854.54 (approx.)
Hence, option (A) 5400 is incorrect.
The correct answer is option (E) None of these.
Principal amount (P) = Rs. 8400
Number of installments (n) = 2
Rate of interest (r) = 20% compounded annually
To find: Value of each installment
Formula used:
EMI formula = [P x r x (1 + r)^n] / [(1 + r)^n – 1]
Calculation:
As the loan is to be paid in two equal annual installments, the total amount to be paid will be the sum of two installments.
Total amount to be paid = 2 x Value of each installment
Let’s calculate the value of each installment using the EMI formula.
EMI formula = [P x r x (1 + r)^n] / [(1 + r)^n – 1]
= [8400 x 0.2 x (1 + 0.2)^2] / [(1 + 0.2)^2 – 1]
= (8400 x 0.2 x 1.44) / 0.44
= 6912 / 0.44
= Rs. 15709.09 (approx.)
Therefore, the total amount to be paid will be 2 x Rs. 15709.09 = Rs. 31418.18 (approx.)
And, the value of each installment will be Rs. 31418.18 / 2 = Rs. 15709.09 / 2 = Rs. 7854.54 (approx.)
Hence, option (A) 5400 is incorrect.
The correct answer is option (E) None of these.
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Question Description
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