? a man purchased a house valued at 300000. he paid 200000 at the time...
Answer:
Here is the solution:
As we know that
P.V = 300000-200000
P.V = 100000
So,
I = 12 percent/ 2
I= 6 perecnt
and
N = 20
A = ?
Now applying
P.V = A[(1+i)^n-1]/i(1+i)^n
putting values
100000 = A[(1.06)^20-1]/0.06(1.06)^20
A= 8719.66
Hence 8719.66 is the amount of each installation
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? a man purchased a house valued at 300000. he paid 200000 at the time...
Problem:
A man purchased a house valued at $300,000. He paid $200,000 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 installments. If the first installment is paid after 6 months from the date of purchase, then what is the amount of each installment?
Solution:
1. Understanding the problem:
- The man purchased a house valued at $300,000.
- He paid $200,000 at the time of purchase.
- The remaining balance needs to be paid in 20 equal half-yearly installments.
- The interest rate is 12% p.a, compounded half-yearly.
- The first installment is paid after 6 months from the date of purchase.
2. Calculating the remaining balance:
- The remaining balance to be paid is $300,000 - $200,000 = $100,000.
3. Calculating the interest:
- The interest rate is 12% p.a, compounded half-yearly.
- The interest is calculated as A = P(1 + r/n)^(nt) - P, where A is the future value, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
- In this case, P = $100,000, r = 12% = 0.12, n = 2 (compounded half-yearly), and t = 20 (total number of installments).
- Calculating A: A = $100,000(1 + 0.12/2)^(2*20) - $100,000 = $202,000.77
4. Calculating the amount of each installment:
- The total amount to be paid, including the interest, is $202,000.77.
- The total number of installments is 20.
- Therefore, the amount of each installment is $202,000.77 / 20 = $10,100.04.
Answer:
The amount of each installment is $10,100.04.
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