A man purchased a house valued at Rs. 300000.He paid Rs. 200000 at the...
Calculation of Installment Amount
The man purchased a house valued at Rs. 300000 and made a down payment of Rs. 200000. He agreed to pay the balance with interest at 12% per annum compounded half yearly in 20 equal half-yearly installments. The first installment is paid after six months from the date of purchase. We need to calculate the amount of each installment.
Calculation of Total Amount Payable
Let's first calculate the total amount payable by the man.
Principal amount (P) = Rs. 100000 (Rs. 300000 - Rs. 200000)
Rate of interest (r) = 12% per annum
Time period (t) = 20 half years
Interest rate per half year (i) = 6% (12%/2)
Number of compounding periods (n) = 40 (20 x 2)
Using the formula for compound interest, we can calculate the total amount payable (A) as:
A = P(1 + i)^n
A = Rs. 100000(1 + 0.06)^40
A = Rs. 362237.64
Calculation of Installment Amount
Now, we can calculate the installment amount using the formula for present value of an annuity.
Present value of annuity (PV) = A[(1 - (1 + i)^-n)/i]
PV = Rs. 362237.64[(1 - (1 + 0.06)^-40)/0.06]
PV = Rs. 362237.64[14.877]
PV = Rs. 5395376.34
Each installment amount can be calculated by dividing the present value of annuity by the number of installments.
Installment amount = PV/20
Installment amount = Rs. 269768.82
Conclusion
Therefore, the amount of each installment is Rs. 269768.82.