##### Mortgage Financing question

 Mathematics Tutor: None Selected Time limit: 1 Day

Question #3 – Mortgage Financing

Samantha purchased a \$129,000 home with 30-year term, 6% rate mortgage. At closing she paid a \$10,000 down payment, requiring her to purchase private mortgage insurance (PMI) at a cost of \$25 per month. Calculate Samantha’s monthly mortgage plus PMI payment.

Aug 19th, 2015

The total price of the home is \$129,000, but since the down payment was \$10,000, she only had to take a mortgage of \$129,000-10,000= \$119,000. This is the principal amount

The rate of the loan is 6% annually, but since we are calculating monthly payments we need to convert it to a monthly rate. We do that by dividing the annual rate by 12; Monthly rate: 6%/12 = 0.5%= 0.005 (converting from percent to decimal)

Also, we need to treat the time in terms of months. 30 years corresponds to 30*12 = 360 months.

We now have all the necessary information to calculate the monthly mortgage payment using the formula:

M = P [ i*(1 + i)^n ] / [ (1 + i)^n – 1] {can get this formula in textbooks or http://www.nerdwallet.com/blog/finance/mortgage/faq/calculate-monthly-mortgage-payment/}

Where M is the monthly payment, P is the principal, i is the monthly rate and n is the time in months.

Plugging in all the components that we calculated above (in bold) gives:

M = 119,000 * [0.005*(1+.005)^360]/ [ (1+.005)^360 - 1] = \$713.46512...

However, don't forget to add the monthly insurance of \$25, giving us a final answer of:

\$713.46512 + \$25 = \$738.46512 which would most likely be rounded to \$738.47 per month

Please let me know if you need any clarification. Always glad to help!
Aug 19th, 2015

Great job, quick and accurate work.

Aug 19th, 2015

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Aug 19th, 2015
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Aug 19th, 2015
May 25th, 2017
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