What is the difference in monthly payments between a 15-year loan at 5% and a 30-year loan at 6% for a $140,000 mortgage?

What is the difference in monthly payments between a 15-year loan at 5% and a 30-year loan at 6% for a $140,000 mortgage?

• A. $267
• B. $150
• C. $350
• D. $425

Answer: (A)

To determine the difference in monthly payments between a 15-year loan at 5% and a 30-year loan at 6% for a $140,000 mortgage, we need to calculate the monthly payment for each scenario using the mortgage payment formula. The formula for the monthly mortgage payment \( M \) can be expressed as: \[ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \] where: - \( P \) is the principal loan amount, - \( r \) is the monthly interest rate (annual rate / 12), - \( n \) is the total number of payments (loan term in months). **For the 15-year loan at 5%:** - Principal \( P = 140,000 \) - Annual interest rate = 5%, so monthly interest rate \( r = \frac{5\%}{12} = 0.004167 \) - Number of payments \( n = 15 \times 12 = 180 \) Plugging in the values: \[ M_{15} = 140,000 \times \frac{0.004167(1 + 0.004167

To determine the difference in monthly payments between a 15-year loan at 5% and a 30-year loan at 6% for a $140,000 mortgage, we need to calculate the monthly payment for each scenario using the mortgage payment formula. The formula for the monthly mortgage payment ( M ) can be expressed as:

[

M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}

]

where:

• ( P ) is the principal loan amount,

• ( r ) is the monthly interest rate (annual rate / 12),

• ( n ) is the total number of payments (loan term in months).

For the 15-year loan at 5%:

• Principal ( P = 140,000 )

• Annual interest rate = 5%, so monthly interest rate ( r = \frac{5%}{12} = 0.004167 )

• Number of payments ( n = 15 \times 12 = 180 )

Plugging in the values:

[

M_{15} = 140,000 \times \frac{0.004167(1 + 0.004167