To calculate how much you can offer for the house, you need to first determine the total amount of the loan that the bank is willing to give you. This will depend on your annual salary, the monthly compounding rate, and the loan term.
First, convert your annual salary to monthly income by dividing it by 12: $48,000 / 12 = $4,000 per month.
Next, calculate the monthly compounding rate by dividing it by 100: 50bps / 100 = 0.005.
Then, multiply your monthly income by the monthly compounding rate to determine the monthly loan payment that the bank is willing to offer you: $4,000 * 0.005 = $20.
Finally, multiply the monthly loan payment by the number of months in the loan term (360 months for a 30-year loan) to determine the total loan amount: $20 * 360 = $7,200.
To this amount, you need to add the closing costs, which are estimated to be 5% of the loan value. So, multiply the loan amount by 0.05 to determine the closing costs: $7,200 * 0.05 = $360.
Now that you know the total loan amount and closing costs, you can subtract them from the amount you have available for a down payment and closing costs to determine how much you can offer for the house: $30,000 - $7,200 - $360 = $22,440.