A man purchased a house valued at 3,00,000. He paid 200.000 at the tim...
Calculation of Total Payment
The total payment that the man has to make for the purchase of the house can be calculated as follows:
- Amount paid at the time of purchase = 2,00,000
- Balance amount to be paid = 3,00,000 - 2,00,000 = 1,00,000
The interest rate is 12% per annum, compounded half-yearly. Therefore, the interest rate per half-year is:
- Rate of interest per half-year = 12/2 = 6% = 0.06
The duration of payment is 20 equal half-yearly instalments. Therefore, the number of instalments is:
- Number of instalments = 20
Calculation of Instalment Amount
The instalment amount can be calculated using the following formula:
- Instalment Amount = (P x R)/(1 - (1 + R)^(-N))
Where,
- P = Principal amount (balance amount to be paid)
- R = Rate of interest per half-year
- N = Number of instalments
Substituting the given values, we get:
- Instalment Amount = (1,00,000 x 0.06)/(1 - (1 + 0.06)^(-20))
- Instalment Amount = 8,821.09 (approx.)
Therefore, the amount of each instalment is Rs. 8,821.09 (approx.).
Calculation of First Instalment Amount
The first instalment is paid after six months from the date of purchase. Therefore, interest will be charged for the first six months. The first instalment amount can be calculated as follows:
- Interest for the first six months = (P x R)/2 = (1,00,000 x 0.06)/2 = 3,000
- Principal amount for the first instalment = Instalment Amount - Interest for the first six months
- Principal amount for the first instalment = 8,821.09 - 3,000 = 5,821.09 (approx.)
Therefore, the amount of the first instalment is Rs. 5,821.09 (approx.).
Note: The given values of log 10.6 and log 31.19 are not required for the calculation of the instalment amount and the first instalment amount.