Question

An investor has $60,000 to invest in a $280,000 property. He can obtain either a $220,000 loan at 9.5 percent for 20 years or a $180,000 loan at 9 percent for 20 years and a second mortgage for $40,000 at 13 percent for 20 years. All loans require monthly payments and are fully amortizing.

1. Which alternative should the borrower choose, assuming he will own the property for the full loan term?

2. Would your answer change if the borrower plans to own the property only five years?

Answer 1

please ask if any query

Answer 2

To determine which loan option the borrower should choose, we need to compare the total cost of each option over the loan term. The total cost includes both the monthly payments and the total interest paid.

Option 1: $220,000 loan at 9.5% for 20 years Monthly Payment: Calculate using the formula for fully amortizing loans. Loan Amount: $220,000 Interest Rate: 9.5% per year (0.095 per month) Loan Term: 20 years (240 months)

Option 2: $180,000 loan at 9% for 20 years + $40,000 second mortgage at 13% for 20 years Monthly Payment for Loan 1: Calculate using the formula for fully amortizing loans. Loan Amount: $180,000 Interest Rate: 9% per year (0.09 per month) Loan Term: 20 years (240 months)

Monthly Payment for Loan 2: Calculate using the formula for fully amortizing loans. Loan Amount: $40,000 Interest Rate: 13% per year (0.13 per month) Loan Term: 20 years (240 months)

Now, let's calculate the total cost of each option over the loan term.

For Option 1: Total Cost = (Monthly Payment for Loan 1) * 240 (months) + (Total Interest Paid for Loan 1)

For Option 2: Total Cost = (Monthly Payment for Loan 1) * 240 (months) + (Total Interest Paid for Loan 1) + (Monthly Payment for Loan 2) * 240 (months) + (Total Interest Paid for Loan 2)

Compare the total costs of both options to determine which one is more favorable for the borrower.

If the borrower plans to own the property only for five years, we can still calculate the total cost of each option over this period and compare them. However, it's worth noting that the difference in total cost may be less significant for a shorter ownership period. The borrower may want to consider other factors such as flexibility, future plans, and potential changes in interest rates before making a decision.