Before we can use the PMT formula, we need to figure out some of our parameters.
(a)
The 20% down payment is calculated by:
235,000 * 20% = $47,000
(b)
The financed amount, P, is calculated by:
235,000 - 47,000 = $188,000
(c)
The bank charges 3 points at the time of closing, which would correspond to 3% of the financed amount:
188,000 * 3% = $5,640
(d)
We know that r (the interest rate) is 6.5%, or 0.065. This is expressed as a yearly rate, so we need to convert it to a monthly rate by dividing by 12 months. This means the monthly interest rate (r/n) is approximately 0.065 / 12 = 0.005416.
We also know that the term of the loan, t, is 30 years. We express this in months, so nt = 30 * 12 = 360 months.
(e)
Now we can finally apply the PMT formula:
The PMT formula calculates a monthly payment, so plugging in our parameters gives us:
PMT = 188,000 * (0.005416 / (1 - (1 + 0.005416)^-360)) = $1,185.79
So, the regular payment amount is approximately $1186 when rounded to the nearest dollar.
Use PMT equals StartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis Over left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndFraction
to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $235 comma 000
.
The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 6.5
%.
Complete parts (a) through (e) below.
1 answer