Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest....

Question:

Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 30% down. Assume that the monthly cost to finance $1,000 is $6.00. What are the monthly payments?

Mortgage Financing

Most banks offer mortgages, which are credits to buy some property and while this mortgage is paid this property is in the name of the bank. There are several forms of mortgage loans, among them is the financed mortgage credit, where the financial entity sets an amount of funding which calls funding factor, this factor can be monthly, quarterly, semiannual or annual.

The banks can finance a part of the mortgage according to what is established, normally they ask the client for an initial percentage for the purchase of a property and finance the rest at an annual interest rate but they can also finance the total cost of the mortgage. In the question posed we want to know the monthly payments if we assume that the monthly cost to finance $1,000 is $6.00, for the purchase of a home that has a value of $450,0000 with a 30-year mortgage at an interest rate of 6% assuming that you can put a 30% down payment.

Answer and Explanation:

Extract the data:

Cost of the house: {eq}$450,000 {/eq}

Time of the mortgage: {eq}30 {/eq} years

Interest rate: {eq}6 \% {/eq}

Initial: {eq}30 \% {/eq}

monthly financing for {eq}$1,000 {/eq} is {eq}$6.00 {/eq}

First you must calculate the cost of the down payment if you put down 30% of the cost of the house:

{eq}IP=CP\times \frac{PI}{100} {/eq}

Where:

IP= Initial Payment

PI= percentage of initial

{eq}IP=\$450,000\times \frac{30 \%}{100} {/eq}

Resulting:

{eq}IP=\$450,000\times 0.30 {/eq}

{eq}IP=\$135,000 {/eq}

Now to find out the amount of what the mortgage will be {eq}M {/eq} you subtract from the cost of the house what would be the down payment.

{eq}M= \$450,000 + \$135,000= \$315,000 {/eq}

The question describes that we must assume that for every {eq}\$1,000 {/eq} of monthly financing is paid {eq}\$6.00 {/eq}; you should look for the monthly equivalent factor MEF:

{eq}MEF= \frac{ \$6.00}{ \$1,000}= 0,006 {/eq}

Once the monthly equivalent factor has been found, the financing factor must be calculated using the following equation

{eq}F= \frac{\left ( 1+MEF \right )^{t}\times MEF}{\left ( 1+MEF \right)^{t}-1} {/eq}

Where:

F: Monthly financing factor

t: time, which must be multiplied by {eq}12 {/eq}, which is the number of months in a year

{eq}t= 30years\times 12 months/year= 360months {/eq}

Enter the data into the monthly financing factor equation

{eq}F= \frac{\left( 1+0.006 \right )^{360}\times0.006}{\left ( 1+0.006 \right)^{360}-1} {/eq}

Solving the mathematical calculations will get you there:

{eq}F= \frac{\left( 1.006 \right )^{360}\times0.006}{\left ( 1.006 \right)^{360}-1} {/eq}

{eq}F= \frac{0.051692}{7.615353} {/eq}

{eq}F= 0.0067879 {/eq}

Once the monthly financing factor is obtained, the monthly payment MP will be obtained according to the financing:

{eq}MP= F\times M {/eq}

Enter the values:

{eq}MP= 0.0067879\times \$315,000 {/eq}

{eq}MP= \$2,138.19 {/eq}

{eq}$2,138.19 {/eq} is the monthly payment.


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