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Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.?
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Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . ...
Given:
- House value: Rs. 300000
- Amount paid at the time of purchase: Rs. 200000
- Balance to be paid in 20 equal half-yearly installments
- Interest rate: 12% p.a. compounded half yearly
To find:
Amount of each installment
Formula:
The formula to calculate the installment amount for a loan with compound interest is:
Installment Amount = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where,
P = Principal amount (balance to be paid)
r = Interest rate per period (half-yearly in this case)
n = Total number of periods (20 in this case)
Calculation:
1. Calculate the balance amount to be paid after the down payment:
Balance = House value - Amount paid at the time of purchase
= Rs. 300000 - Rs. 200000
= Rs. 100000
2. Convert the interest rate to a decimal and divide it by 2 (as it is compounded half yearly):
Interest rate per period (r) = 12%/2 = 6%/100 = 0.06
3. Calculate the total number of periods:
Total number of periods (n) = 20
4. Substitute the values in the formula to calculate the installment amount:
Installment Amount = (Balance * r * (1 + r)^n) / ((1 + r)^n - 1)
= (100000 * 0.06 * (1 + 0.06)^20) / ((1 + 0.06)^20 - 1)
5. Simplify the equation using the given logarithmic values (log1.06 = 1.0253 and log31.19 = 1.494):
Installment Amount = (100000 * 0.06 * (1.0253)^20) / ((1.0253)^20 - 1)
= (100000 * 0.06 * 31.19) / (31.19 - 1)
= (1860 * 31.19) / 30.19
= 58037.4 / 30.19
≈ 1921.84
Answer:
The amount of each installment is approximately Rs. 1921.84.
None of the given options (a), (b), (c) match the calculated value.
- House value: Rs. 300000
- Amount paid at the time of purchase: Rs. 200000
- Balance to be paid in 20 equal half-yearly installments
- Interest rate: 12% p.a. compounded half yearly
To find:
Amount of each installment
Formula:
The formula to calculate the installment amount for a loan with compound interest is:
Installment Amount = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where,
P = Principal amount (balance to be paid)
r = Interest rate per period (half-yearly in this case)
n = Total number of periods (20 in this case)
Calculation:
1. Calculate the balance amount to be paid after the down payment:
Balance = House value - Amount paid at the time of purchase
= Rs. 300000 - Rs. 200000
= Rs. 100000
2. Convert the interest rate to a decimal and divide it by 2 (as it is compounded half yearly):
Interest rate per period (r) = 12%/2 = 6%/100 = 0.06
3. Calculate the total number of periods:
Total number of periods (n) = 20
4. Substitute the values in the formula to calculate the installment amount:
Installment Amount = (Balance * r * (1 + r)^n) / ((1 + r)^n - 1)
= (100000 * 0.06 * (1 + 0.06)^20) / ((1 + 0.06)^20 - 1)
5. Simplify the equation using the given logarithmic values (log1.06 = 1.0253 and log31.19 = 1.494):
Installment Amount = (100000 * 0.06 * (1.0253)^20) / ((1.0253)^20 - 1)
= (100000 * 0.06 * 31.19) / (31.19 - 1)
= (1860 * 31.19) / 30.19
= 58037.4 / 30.19
≈ 1921.84
Answer:
The amount of each installment is approximately Rs. 1921.84.
None of the given options (a), (b), (c) match the calculated value.
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Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.?
Question Description
Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.?.
Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.?.
Solutions for Pg (4.37) ICAI Q (8) : A man purchased a house valued at Rs. 300000 . He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% p.a. compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase the the amount of each instalment is (given : log1.06=1.0253 and log31.19=1.494)? options are : (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d)None of these.? in English & in Hindi are available as part of our courses for Quant.
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