Graeme Is Purchasing A Home For $200,000 And Has A 25% Down

Question

Graeme Is Purchasing A Home For 200000 And Has A 25 Down Payment Graeme is purchasing a home for $200,000 with a 25% down payment. The seller has an existing mortgage with a balance of $90,000 at an attractive rate of 3.75% for the next 5 years. Graeme has two options: (1) take out a single mortgage for the full required amount at a rate of 4.25%, or (2) assume the $90,000 mortgage and take out a second mortgage for the remaining difference at a rate of 4.75%. The goal is to determine which option results in the best overall rate.

Dr. Jack HW Helper · Accepted Answer

In analyzing Graeme's mortgage options, it is essential to understand how each alternative affects the overall effective interest rate, which reflects the cost of financing the home purchase. This detailed examination considers the structure of each option, the impact of assuming the existing mortgage, and the implications for total borrowing costs. Step 1: Determine the total purchase price and down payment The purchase price of the home is $200,000, with a 25% down payment. Calculating the down payment: $$ \$200,000 \times 0.25 = \$50,000 $$ Thus, Graeme's down payment is $50,000. The remaining amount to finance is: $$ \$200,000 - \$50,000 = \$150,000 $$ Step 2: Analyze Option 1 – Single mortgage at 4.25% In this scenario, Graeme obtains a single mortgage for the full $150,000 at an interest rate of 4.25%. Step 3: Analyze Option 2 – Assume the existing mortgage and take out a second mortgage In this scenario, Graeme assumes the existing mortgage with a balance of $90,000 at an attractive rate of 3.75%. The remaining amount to finance is: $$ \$150,000 - \$90,000 = \$60,000 $$ Graeme then takes out a second mortgage for $60,000 at an interest rate of 4.75%. Step 4: Calculate the weighted average interest rate for Option 2 To determine which option results in the best overall rate, we calculate the weighted average interest rate for the combined mortgages under Option 2, considering the amounts borrowed at each rate. Total debt in Option 2: $$ \$90,000 + \$60,000 = \$150,000 $$ Weighted average interest rate: $$ \frac{\left( \$90,000 \times 3.75\% \right) + \left( \$60,000 \times 4.75\% \right)}{\$150,000} $$ Calculate numerator: $$ \$90,000 \times 0.0375 = \$3,375 $$ $$ \$60,000 \times 0.0475 = \$2,850 $$ Sum: $$ \$3,375 + \$2,850 = \$6,225 $$ Compute overall rate: $$ \frac{\$6,225}{\$150,000} = 0.0415 = 4.15\% $$ Step 5: Comparison of the two options - Option 1: Single mortgage at 4.25%. - Option 2: Assumed existing mortgage plus second mortgage with weighted avera

Graeme Is Purchasing A Home For $200,000 And Has A 25% Down

Graeme Is Purchasing A Home For 200000 And Has A 25 Down Payment

Paper For Above instruction

Step 1: Determine the total purchase price and down payment

Step 2: Analyze Option 1 – Single mortgage at 4.25%

Step 3: Analyze Option 2 – Assume the existing mortgage and take out a second mortgage

Step 4: Calculate the weighted average interest rate for Option 2

Step 5: Comparison of the two options

Step 6: Additional considerations

Conclusion

References