Mortgage Financing question
Mathematics

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Samantha purchased a $129,000 home with 30year 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.
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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 $129,00010,000= $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/calculatemonthlymortgagepayment/}
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!Great job, quick and accurate work.
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