Explanation

To calculate the monthly savings from refinancing, we need to compute the monthly payments for both mortgages and find the difference.

Step 1: Calculate monthly payment for original mortgage (5% rate)

• Principal: $250,000
• Annual interest rate: 5%
• Monthly interest rate: 5%/12 = 0.41667%
• Number of payments: 30 years × 12 = 360

Using the mortgage payment formula: $PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$

Where:

• P = $250,000
• r = 0.05/12 = 0.0041667
• n = 360

$PMT_{5\%} = 250,000 \times \frac{0.0041667(1.0041667)^{360}}{(1.0041667)^{360} - 1}$ $PMT_{5\%} = 250,000 \times \frac{0.0041667 \times 4.467744}{4.467744 - 1}$ $PMT_{5\%} = 250,000 \times \frac{0.018616}{3.467744}$ $PMT_{5\%} = 250,000 \times 0.005368$ PMT_{5\%} = \`$1`,342.05

Step 2: Calculate monthly payment for new mortgage (4% rate)

• Principal: $250,000
• Annual interest rate: 4%
• Monthly interest rate: 4%/12 = 0.33333%
• Number of payments: 30 years × 12 = 360

$PMT_{4\%} = 250,000 \times \frac{0.0033333(1.0033333)^{360}}{(1.0033333)^{360} - 1}$ $PMT_{4\%} = 250,000 \times \frac{0.0033333 \times 3.313}{3.313 - 1}$ $PMT_{4\%} = 250,000 \times \frac{0.011043}{2.313}$ $PMT_{4\%} = 250,000 \times 0.004774$ PMT_{4\%} = \`$1`,193.54

Step 3: Calculate monthly savings

$\text{Savings} = PMT_{5\%} - PMT_{4\%}$ \text{Savings} = 1,342.05 - 1,193.54 = \`$148.51`

The closest option to $148.51 is USD 145.

Answer: A