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Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
- a)45311
- b)51311
- c)33130
- d)40991
Correct answer is option 'B'. Can you explain this answer?
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Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounde...
Calculation of Total Interest Paid
1. Interest for the first year:
- Anil borrows Rs 2 lakhs at 8% per annum, compounded half-yearly.
- The interest for the first year is calculated on the principal amount of Rs 2 lakhs.
- Using the formula for compound interest: A = P(1 + r/n)^(nt)
- A = 2,00,000(1 + 0.08/2)^(2*1)
- A = 2,00,000(1 + 0.04)^2
- A = 2,00,000(1.04)^2
- A = 2,00,000(1.0816)
- A = Rs 2,16,320
- Total interest paid at the end of the first year = Rs 2,16,320 - Rs 2,00,000 = Rs 16,320
2. Repayment at the end of the first year:
- Anil repays Rs 10,320 at the end of the first year.
- The interest component in the repayment = Rs 10,320 - Rs 8,000 = Rs 2,320
3. Outstanding amount at the end of the first year:
- Principal amount remaining after the first year = Rs 2,00,000 - Rs 10,320 = Rs 1,89,680
4. Interest for the second year:
- Interest calculated on the outstanding amount of Rs 1,89,680 for the second year.
- Using the compound interest formula: A = P(1 + r/n)^(nt)
- A = 1,89,680(1 + 0.08/2)^(2*1)
- A = 1,89,680(1.04)^2
- A = 1,89,680(1.0816)
- A = Rs 2,04,414.848
- Total interest paid at the end of the second year = Rs 2,04,414.848 - Rs 1,89,680 = Rs 14,734.848
5. Outstanding amount at the end of the second year:
- Principal amount remaining after the second year = Rs 1,89,680 - Rs 14,734.848 = Rs 1,74,945.152
6. Interest for the third year:
- Interest calculated on the outstanding amount of Rs 1,74,945.152 for the third year.
- Using the compound interest formula: A = P(1 + r/n)^(nt)
- A = 1,74,945.152(1 + 0.08/2)^(2*1)
- A = 1,74,945.152(1.04)^2
- A = 1,74,945.152(1.0816)
- A = Rs 1,88,943.905
- Total interest paid at the end of the third year = Rs 1,88,
1. Interest for the first year:
- Anil borrows Rs 2 lakhs at 8% per annum, compounded half-yearly.
- The interest for the first year is calculated on the principal amount of Rs 2 lakhs.
- Using the formula for compound interest: A = P(1 + r/n)^(nt)
- A = 2,00,000(1 + 0.08/2)^(2*1)
- A = 2,00,000(1 + 0.04)^2
- A = 2,00,000(1.04)^2
- A = 2,00,000(1.0816)
- A = Rs 2,16,320
- Total interest paid at the end of the first year = Rs 2,16,320 - Rs 2,00,000 = Rs 16,320
2. Repayment at the end of the first year:
- Anil repays Rs 10,320 at the end of the first year.
- The interest component in the repayment = Rs 10,320 - Rs 8,000 = Rs 2,320
3. Outstanding amount at the end of the first year:
- Principal amount remaining after the first year = Rs 2,00,000 - Rs 10,320 = Rs 1,89,680
4. Interest for the second year:
- Interest calculated on the outstanding amount of Rs 1,89,680 for the second year.
- Using the compound interest formula: A = P(1 + r/n)^(nt)
- A = 1,89,680(1 + 0.08/2)^(2*1)
- A = 1,89,680(1.04)^2
- A = 1,89,680(1.0816)
- A = Rs 2,04,414.848
- Total interest paid at the end of the second year = Rs 2,04,414.848 - Rs 1,89,680 = Rs 14,734.848
5. Outstanding amount at the end of the second year:
- Principal amount remaining after the second year = Rs 1,89,680 - Rs 14,734.848 = Rs 1,74,945.152
6. Interest for the third year:
- Interest calculated on the outstanding amount of Rs 1,74,945.152 for the third year.
- Using the compound interest formula: A = P(1 + r/n)^(nt)
- A = 1,74,945.152(1 + 0.08/2)^(2*1)
- A = 1,74,945.152(1.04)^2
- A = 1,74,945.152(1.0816)
- A = Rs 1,88,943.905
- Total interest paid at the end of the third year = Rs 1,88,
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Community Answer
Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounde...
“Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10,320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year.”
This means, the amount paid by Anil at the end of the third year = (2,00,000 × 1.042 − 10,320) × 1.044 = 2,40,990.8634 ≅ 2,40,991
So the total amount paid by Anil = 10,320 + 2,40,991 = 2,51,311
So the total interest paid = 2,51,311 − 2,00,000 = 51,311
This means, the amount paid by Anil at the end of the third year = (2,00,000 × 1.042 − 10,320) × 1.044 = 2,40,990.8634 ≅ 2,40,991
So the total amount paid by Anil = 10,320 + 2,40,991 = 2,51,311
So the total interest paid = 2,51,311 − 2,00,000 = 51,311
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Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest toa)45311b)51311c)33130d)40991Correct answer is option 'B'. Can you explain this answer?
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