A man purchased a house valued at Rs. 300000. He paid Rs. 200000 at th...
Calculation of Each Instalment: Given:- House value: Rs. 300000
- Amount paid at the time of purchase: Rs. 200000
- Interest rate: 12% per annum compounded half yearly
- Number of instalments: 20
Calculating the Remaining Balance:The remaining balance on the house after the initial payment of Rs. 200000 can be calculated using the compound interest formula:
Balance = Principal x (1 + (r/n))^(nt) - P
Where:
- P = Principal amount paid initially = Rs. 200000
- r = Annual interest rate = 12%
- n = Number of compounding periods per year = 2 (half yearly)
- t = Total number of years for repayment = 20/2 = 10 years
By substituting the values, we get:
Balance = 200000 x (1 + (0.12/2))^(2*10) - 200000
Balance = 200000 x (1 + 0.06)^20 - 200000
Balance = 200000 x (1.06)^20 - 200000
Balance ≈ 300000 - 200000
Balance ≈ Rs. 100000
Calculating Each Instalment:To calculate the amount of each instalment, we divide the remaining balance by the present value annuity factor for 20 periods at 6% interest rate (half of 12%):
Each Instalment = Remaining Balance / Present Value Annuity Factor
Each Instalment = Rs. 100000 / Present Value Annuity Factor
By using the formula for Present Value Annuity Factor, we can calculate the amount of each instalment.