The price of a condominium is $132 comma 000
.
The bank requires a 5% down payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortgage at 9
%.
Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below.
PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
There are a few steps to solving this problem. Here's what you need to do:
(a) Find the down payment.
The bank requires a 5% down payment, so simply take 5% of the price of the condominium:
0.05 * $132000 = $6600.
(b) Find the number of points.
One point is simply 1% of the loan amount. Since the loan amount is the price of the condominium minus the down payment, and 1 point is charged at closing,
loan amount = $132000 - $6600 = $125400.
One point is then 0.01 * $125400 = $1254.
(c) Calculate the total cost.
The total cost at closing would be the down payment plus the points charged, or $6600 + $1254 = $7854.
(d) Determine the PMT or regular payment amount.
This is where the given formula comes in. The values you need are:
P = loan amount = $125400.
r = annual interest rate = 0.09.
n = number of payments per year = 12 (for monthly payments).
t = number of years = 30.
Plug these values into the formula:
PMT = [$125400 * (0.09/12)] / [1 - (1 + 0.09/12)^-(12*30)]
This is a bit complex to solve without a calculator, but when you do, you'll get the monthly payment amount.
(e) Understand what you've found.
The down payment and one point are costs you have to pay upfront, at closing. The PMT is the amount you have to pay monthly for 30 years to repay the loan from the bank.
To find the regular payment amount, we need to use the PMT formula provided:
PMT = P * (r / n) / (1 - (1 + (r / n))^(-nt))
where:
P = Principal loan amount = $132,000
r = Annual interest rate = 9% = 0.09
n = Number of payments per year = 12 (assuming monthly payments)
t = Number of years = 30
Now, let's calculate the regular payment amount step-by-step:
(a) Calculate the down payment:
Down payment = 5% of $132,000 = 0.05 * $132,000 = $6,600
(b) Calculate one point:
One point = 1% of $132,000 = 0.01 * $132,000 = $1,320
(c) Calculate the loan amount:
Loan amount = Price of the condominium - Down payment - One point
Loan amount = $132,000 - $6,600 - $1,320 = $124,080
(d) Calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 0.09 / 12 = 0.0075
(e) Calculate the regular payment amount using the PMT formula:
PMT = $124,080 * (0.0075 / 12) / (1 - (1 + (0.0075 / 12))^(-12*30))
PMT = $927.22 (rounded to the nearest cent)
Therefore, the regular payment amount for the 30-year fixed-rate mortgage is $927.22.