you can afford a $900 per month mortgage paym...
you can afford a $900 per month mortgage payment. you can get a loan at 6.8% interest for 20 years. do not round numbers while working on the problem. only round the final answer. since we are working with money, round to the cent. what is the largest loan you can afford? how much total money will you pay the loan company? how much of that money is interest?
Answer
# Explanation:
## Step1: Identify the relevant formula
The formula for the present - value of an ordinary annuity is $PV = PMT\times\frac{1-(1 + r)^{-n}}{r}$, where $PV$ is the present value (loan amount), $PMT$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of periods.
The annual interest rate $i = 6.8\%=0.068$. The monthly interest rate $r=\frac{0.068}{12}$. The number of years $t = 20$, so the number of months $n=20\times12 = 240$, and $PMT = 900$.
## Step2: Calculate the loan amount
$r=\frac{0.068}{12}\approx0.005667$
$PV = 900\times\frac{1-(1 + 0.005667)^{-240}}{0.005667}$
First, calculate $(1 + 0.005667)^{-240}\approx0.26777$.
Then, $1-(1 + 0.005667)^{-240}=1 - 0.26777 = 0.73223$.
$\frac{1-(1 + 0.005667)^{-240}}{0.005667}=\frac{0.73223}{0.005667}\approx129.209$.
$PV=900\times129.209 = 116288.10$.
## Step3: Calculate the total amount paid
The total amount paid to the loan company is the monthly payment times the number of months.
$Total\ paid=PMT\times n=900\times240 = 216000$.
## Step4: Calculate the interest amount
The interest amount is the total amount paid minus the loan amount.
$Interest = Total\ paid - PV=216000 - 116288.10=99711.90$.
# Answer:
The largest loan you can afford: $\$116288.10$
The total money you will pay the loan company: $\$216000.00$
The amount of money that is interest: $\$99711.90$