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The freemans have decided to build a new house. The contractor quoted them a price of $135,700. The taxes on the house will be $3450 per year , and homeowner's insurance will be $350 per year. They have apploed for a conventional loan from a local bank. The bank os requiring a 25% down payment , and the interesr rate on the loan os 9.5% . Determine the amount of the down payment. Determine the monthly oayment of principal and interest for a 30 -year loan at 9.5%. Determine their total monthly payment, including insurance and taxes. if they started planning to sace 6 years ago to help with the downpayment, how much should they have invested quaterly in a sinking fund with a 3.6 % interest rate compunded quarterly in order to accumulate $20,000

User Kivikall
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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)

User LawrenceGS
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