Question

Tyler wants to buy a beach house as part of his investment portfolio. After searching the coast for a nice home, he finds a house with a great view and a hefty price of $4,500,000. Tyler will need to borrow from the bank to pay for this house. Mortgage rates are based on the length of the loan, and a local bank is advertising fifteen-year loans with monthly payments at 7.125%, twenty-year loans with monthly payments at 7.25%, and thirty-year loans with monthly payments at 7.375%. What is the monthly payment of principal and interest for each loan? Tyler believes that the property will be worth $5,500,000 in five years. Ignoring taxes and real estate commissions, if Tyler sells the house after fiveyears, what will be the difference in the selling price and the remaining principal on the loan for each of the three loans?

Answer 1

To calculate the monthly payment of principal and interest for each loan, use the formula PMT = P × r ÷ (1 - (1 + r)^(-n)). The monthly payments for the 15-year, 20-year, and 30-year loans are $40,668.65, $31,127.32, and $27,937.50 respectively. The difference between the selling price and the remaining principal on the loan after five years is $3,209,088.84 for the 15-year loan, $3,459,470.57 for the 20-year loan, and $3,551,474.94 for the 30-year loan.

Step-by-step explanation:

To calculate the monthly payment of principal and interest for each loan, we can use the formula for the monthly payment of a mortgage loan. The formula is:

PMT = P × r ÷ (1 - (1 + r)^(-n))

Where PMT is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments. Using this formula, the monthly payment for each loan is as follows:

• 15-year loan: $40,668.65
• 20-year loan: $31,127.32
• 30-year loan: $27,937.50

To calculate the difference between the selling price and the remaining principal on the loan after five years, we subtract the remaining principal from the selling price. The remaining principal can be found by calculating the present value of the remaining loan payments. Assuming the interest rates remain constant, the difference for each loan is as follows:

• 15-year loan: $3,209,088.84
• 20-year loan: $3,459,470.57
• 30-year loan: $3,551,474.94