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A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is?
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A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at ...
Calculation of Cash Down Price
Given
- Down payment made in cash = Rs. 20,000
- Yearly payment for 25 years = Rs. 4,000
- Rate of interest = 5% p.a
Calculation of Total Payment
The total payment made by the person can be calculated using the formula for the sum of an annuity.
Let A be the yearly payment, r be the rate of interest, and n be the number of years.
Using the formula for the sum of an annuity, the total payment made by the person can be calculated as:
Total payment = A x ((1 + r)^n - 1) / r
Substituting the given values, we get:
Total payment = Rs. 4,000 x ((1 + 0.05)^25 - 1) / 0.05
Total payment = Rs. 1,57,734.86
Calculation of Principal Amount
The principal amount can be calculated using the formula for the present value of an annuity.
Let A be the yearly payment, r be the rate of interest, and n be the number of years.
Using the formula for the present value of an annuity, the principal amount can be calculated as:
Principal amount = A x ((1 - (1 + r)^-n) / r)
Substituting the given values, we get:
Principal amount = Rs. 4,000 x ((1 - (1 + 0.05)^-25) / 0.05)
Principal amount = Rs. 64,487.99
Calculation of Cash Down Price
The cash down price is the initial payment made in cash.
Therefore, the cash down price can be calculated as:
Cash down price = Total payment - Principal amount
Substituting the values, we get:
Cash down price = Rs. 1,57,734.86 - Rs. 64,487.99
Cash down price = Rs. 93,246.87
Conclusion
Therefore, the cash down price of the house is Rs. 93,246.87.
Community Answer
A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at ...
To find the cash down price of the house, we need to determine the present value of the future payments.
Given:
Annual payment (A) = Rs. 4000
Interest rate (r) = 5% = 0.05
Number of years (n) = 25
We can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^(-n)) / r]
Substituting the given values:
PV = 4000 * [(1 - (1 + 0.05)^(-25)) / 0.05]
Using a calculator, we can evaluate this expression:
PV ≈ 4000 * [(1 - 0.3894) / 0.05]
≈ 4000 * [0.6106 / 0.05]
≈ 4000 * 12.212
PV ≈ Rs. 48,848
Therefore, the cash down price of the house is approximately Rs. 48,848.
Given:
Annual payment (A) = Rs. 4000
Interest rate (r) = 5% = 0.05
Number of years (n) = 25
We can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^(-n)) / r]
Substituting the given values:
PV = 4000 * [(1 - (1 + 0.05)^(-25)) / 0.05]
Using a calculator, we can evaluate this expression:
PV ≈ 4000 * [(1 - 0.3894) / 0.05]
≈ 4000 * [0.6106 / 0.05]
≈ 4000 * 12.212
PV ≈ Rs. 48,848
Therefore, the cash down price of the house is approximately Rs. 48,848.
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A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is?
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A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is?.
A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person bought a house paying Rs. 20000 in cash down and Rs. 4000 at the end of each year for 25 years at 5% p.a CI. The cash down price is?.
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