Final answer:
The cash price of the house is RM 580,006.87. The total interest charged is RM 241,993.13. The outstanding balance if Mr Hashimi decides to settle the loan immediately after the 250th payment is RM 132,204.01.
Step-by-step explanation:
To find the cash price of the house, we need to calculate the present value of the monthly payments.
The formula to find the present value of an annuity is:
PV = PMT x (1 - (1 + r)^(-n)) / r
Where PV is the present value, PMT is the monthly payment, r is the interest rate per period (in this case, monthly), and n is the number of periods (in this case, 25 years x 12 months).
Plugging in the values, we have:
PV = 980 x (1 - (1 + 0.06/12)^(-25*12)) / (0.06/12)
PV = 580,006.87
So, the cash price of the house is 580,006.87.
To find the total interest charged, we subtract the cash price of the house from the total amount paid over 25 years:
Total Interest = (Monthly Payment x Number of Payments) - Cash Price of the House
Total Interest = (980 x 25 x 12) - 580,006.87
Total Interest = 241,993.13
So, the total interest charged is 241,993.13.
If Mr Hashimi decides to settle the loan immediately after the 250th payment, we need to calculate the remaining balance.
The formula to find the remaining balance after n months is:
Remaining Balance = PV x (1 + r)^n - PMT x ((1 + r)^n - 1) / r
Plugging in the values, we have:
Remaining Balance = 580,006.87 x (1 + 0.06/12)^(25*12 - 250) - 980 x ((1 + 0.06/12)^(25*12 - 250) - 1) / (0.06/12)
Remaining Balance = 132,204.01
So, the outstanding balance if Mr Hashimi decides to settle the loan immediately after the 250th payment is 132,204.01.