Mortgage Financing question

Mathematics
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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

Hi there! Thank you for the opportunity to help you with your question!

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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