Answer: USD 145

## 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**

Author: LeetQuiz .