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Leela takes a loan of Rs. 8400 at 10% p.a. compounded annually which is to be repaid in two equal annual installments. One at the end of one year and the other at the end of the second year. The value of each installment is?
- a)4200
- b)4140
- c)4840
- d)5640
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Leela takes a loan of Rs. 8400 at 10% p.a. compounded annually which i...
8400 = x*(210/121) => 4840
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Leela takes a loan of Rs. 8400 at 10% p.a. compounded annually which i...
Given:
Loan amount = Rs. 8400
Rate of interest = 10% p.a. compounded annually
Time period = 2 years
Installments = 2 equal annual installments
To find: Value of each installment
Concept Used:
The formula to calculate the value of each installment is given by:
EMI = (P x r x (1 + r)^n) / ((1 + r)^n - 1)
where,
P = Loan amount
r = Rate of interest per annum (compounded annually)
n = Number of installments
Calculation:
In this case, the loan amount is to be repaid in two equal annual installments. So, the number of installments (n) = 2.
Let the value of each installment be x.
For the first year, the interest on the loan amount of Rs. 8400 at 10% p.a. compounded annually will be:
Interest = P x (r/100) = 8400 x (10/100) = Rs. 840
So, the amount to be repaid at the end of the first year = Principal + Interest = Rs. 8400 + Rs. 840 = Rs. 9240
Now, the remaining loan amount to be repaid at the end of the second year = Rs. 9240 - x
For the second year, the interest will be calculated on the remaining loan amount of Rs. 9240 - x.
Interest = (9240 - x) x (10/100) = 924 - 0.1x
So, the amount to be repaid at the end of the second year = Remaining loan amount + Interest = (9240 - x) + (924 - 0.1x) = 8160 - 0.9x
According to the given condition, both the installments are equal. So, we can equate the two amounts to get the value of x.
9240 = 8160 - 0.9x + x
1080 = 0.1x
x = 10800/10
x = Rs. 1080
Therefore, the value of each installment is Rs. 1080.
Hence, option (c) is the correct answer.
Loan amount = Rs. 8400
Rate of interest = 10% p.a. compounded annually
Time period = 2 years
Installments = 2 equal annual installments
To find: Value of each installment
Concept Used:
The formula to calculate the value of each installment is given by:
EMI = (P x r x (1 + r)^n) / ((1 + r)^n - 1)
where,
P = Loan amount
r = Rate of interest per annum (compounded annually)
n = Number of installments
Calculation:
In this case, the loan amount is to be repaid in two equal annual installments. So, the number of installments (n) = 2.
Let the value of each installment be x.
For the first year, the interest on the loan amount of Rs. 8400 at 10% p.a. compounded annually will be:
Interest = P x (r/100) = 8400 x (10/100) = Rs. 840
So, the amount to be repaid at the end of the first year = Principal + Interest = Rs. 8400 + Rs. 840 = Rs. 9240
Now, the remaining loan amount to be repaid at the end of the second year = Rs. 9240 - x
For the second year, the interest will be calculated on the remaining loan amount of Rs. 9240 - x.
Interest = (9240 - x) x (10/100) = 924 - 0.1x
So, the amount to be repaid at the end of the second year = Remaining loan amount + Interest = (9240 - x) + (924 - 0.1x) = 8160 - 0.9x
According to the given condition, both the installments are equal. So, we can equate the two amounts to get the value of x.
9240 = 8160 - 0.9x + x
1080 = 0.1x
x = 10800/10
x = Rs. 1080
Therefore, the value of each installment is Rs. 1080.
Hence, option (c) is the correct answer.
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Leela takes a loan of Rs. 8400 at 10% p.a. compounded annually which i...
8400 = x*(210/121) ⇒ 4840
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