What are the monthly payments on a $950,000 mortgage at 4.8% interest for 15 years?

Prepare for the Statistics, Modeling and Finance Exam. Leverage flashcards and multiple choice questions with detailed explanations. Achieve exam success!

Multiple Choice

What are the monthly payments on a $950,000 mortgage at 4.8% interest for 15 years?

To determine the monthly payments on a mortgage, we can use the formula for the monthly payment on an amortizing loan, which is: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \(M\) is the total monthly mortgage payment, - \(P\) is the principal loan amount, - \(r\) is the monthly interest rate (annual rate divided by 12), - \(n\) is the number of payments (loan term in months). For this scenario: - The principal \(P\) is $950,000. - The annual interest rate is 4.8%, so the monthly interest rate \(r\) would be \(0.048 / 12 = 0.004\). - The loan term of 15 years translates to \(n = 15 \times 12 = 180\) months. Substituting these values into the formula, we get: \[ M = 950000 \cdot \frac{0.004(1 + 0.004)^{180}}{(1 + 0.004)^{180} - 1} \]

To determine the monthly payments on a mortgage, we can use the formula for the monthly payment on an amortizing loan, which is:

[

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

]

where:

  • (M) is the total monthly mortgage payment,

  • (P) is the principal loan amount,

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

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

For this scenario:

  • The principal (P) is $950,000.

  • The annual interest rate is 4.8%, so the monthly interest rate (r) would be (0.048 / 12 = 0.004).

  • The loan term of 15 years translates to (n = 15 \times 12 = 180) months.

Substituting these values into the formula, we get:

[

M = 950000 \cdot \frac{0.004(1 + 0.004)^{180}}{(1 + 0.004)^{180} - 1}

]

More practice questions