Final answer:
The amount of the down payment is $33,925. The monthly payment of principal and interest for a 30-year loan at 9.5% is $960.40. The total monthly payment, including insurance and taxes, is $960.40 + $350/12 + $3450/12.
Step-by-step explanation:
To determine the amount of the down payment, we can use the equation:
Down payment = Purchase price * Down payment percentage
Given that the purchase price is $135,700 and the down payment percentage is 25%, the down payment would be:
Down payment = $135,700 * 0.25 = $33,925
To determine the monthly payment of principal and interest for a 30-year loan at 9.5%, we can use the formula for calculating monthly mortgage payments:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
Plugging in the values, the monthly payment for a 30-year loan at 9.5% would be:
Monthly payment = ($135,700 - $33,925) * (0.095 / 12) / (1 - (1 + 0.095/12)^(-30 * 12))
Finally, to determine the total monthly payment including insurance and taxes, we can add the homeowner's insurance and taxes to the monthly payment:
Total monthly payment = Monthly payment + Homeowner's insurance + Taxes
Given that the homeowner's insurance is $350 per year and the taxes are $3450 per year, the total monthly payment would be:
Total monthly payment = Monthly payment + $350/12 + $3450/12
To calculate the amount the Freemans should have invested quarterly in a sinking fund in order to accumulate $20,000, we can use the formula for compound interest:
Future value = Present value * (1 + (Interest rate / Number of compounding periods))^(Number of compounding periods * Number of years)
Plugging in the values, the equation would be:
$20,000 = Present value * (1 + (0.036 / 4))^((1/4) * 6)
Solving for the present value, the amount the Freemans should have invested quarterly would be:
Present value = $20,000 / (1 + 0.036/4)^(4 * 6)