# You found your dream house. It will cost you $875,000 and you will put down$50,000 as a down...

## Question:

You found your dream house. It will cost you $875,000 and you will put down$50,000 as a down payment. For the rest you get a 30 year 6.00% mortgage.

What will be your monthly mortgage payment (assume no early repayment)?

## Mortgage Payments:

Mortgage payments are one of the most common payments done by an individual. The payments are calculated based on the loan amount, the prevailing rate and the time period of the mortgage.

The monthly mortgage payment would be $4,946.29 The mortgage payments can be calculated from the following expression: {eq}Payment = \dfrac {Loan\:Value}{\dfrac{1-(1+r)^{-n}}{r}} {/eq} The values from the question are: • Payment = ? • Loan Value =$875,000 - $50,000 =$825,000 ( Adjustment for down payment).
• r (rate) = 6% / 12 = 0.50% or 0.005
• n = 30 * 12 = 360

Plugging in the variables in the formula, we have:

{eq}Payment = \dfrac { $825,000}{\dfrac{1-(1+0.005)^{-360}}{0.005}}\\ Payment = \dfrac {$ 825,000}{ 166.7916 }\\ Payment = \$4,946.29 {/eq}