Final answer:
To determine how much Peter should charge for rent of the other half of the duplex, we need to calculate his monthly mortgage payment and then subtract the amount he can afford to spend on his mortgage payment. Peter should increase the rent by $200.
Step-by-step explanation:
To determine how much Peter should charge for rent of the other half of the duplex, we need to calculate his monthly mortgage payment and then subtract the amount he can afford to spend on his mortgage payment. First, we need to find Peter's down payment amount, which is 10% of the purchase price: $226,950 x 0.1 = $22,695. Next, we need to calculate the loan amount: $226,950 - $22,695 = $204,255. To find Peter's monthly mortgage payment, we can use the formula for calculating monthly mortgage payments:
Monthly Mortgage Payment = Loan Amount x Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
Plugging in the values, we have:
Loan Amount = $204,255
Monthly Interest Rate = 6.25% / 12 = 0.0052083
Number of Payments = 30 years x 12 months = 360
Using a calculator, the monthly mortgage payment is approximately $1,257.07. Now, we can subtract 10% of Peter's monthly income from his monthly mortgage payment to find the amount he can afford to spend on his mortgage payment: $2,985 x 0.1 = $298.50. Subtracting this from the mortgage payment, we get: $1,257.07 - $298.50 = $958.57. So, Peter can afford to spend $958.57 on his mortgage payment.
Since Peter wants the rent to cover the remainder of his mortgage payment, he should adjust how much he charges for rent by increasing it to $958.57. Therefore, the correct answer is: a. Peter should increase the rent by $200.