# You are buying your first house for $215,000 and are paying $30,000 as a down payment. You have...

## Question:

You are buying your first house for $215,000 and are paying $30,000 as a down payment. You have arranged to finance the remaining $185,000 with a 30-year mortgage that has a 6.5% nominal interest rate and monthly payments. What are the equal monthly payments you must make?

## Annuity Formula:

A formula that considers the loan amount as the present value and, based on this current value, computes the periodic mortgage outlay is the annuity formula. The present value represents the cash inflows.

## Answer and Explanation: 1

Calculation of monthly payment:

{eq}\begin{align*} {\rm\text{Monthly payment}}& = \frac{{{\rm\text{Loan}} \times {\rm\text{Interest rate}} \times {{(1 + {\rm\text{Interest rate}})}^{{\rm\text{Number of periods}}}}}}{{{{(1 + {\rm\text{Interest rate}})}^{{\rm\text{Number of periods}}}} - 1}}\\ & = \frac{{185,000 \times 0.065/12 \times {{(1 + 0.065/12)}^{30\times12}}}}{{{{(1 + 0.065/12)}^{30\times12}} - 1}}\\ & = \frac{{1,002.0833\times6.9917980573 }}{{5.9917980573}}\\ &= \$ 1,169.36 \end{align*} {/eq}

Required Answer: $1,169.36

#### Learn more about this topic:

from

Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.