Question

Shelley purchased a home in Maryland Heights, MO, for $204,000. Her down payment was 20% of the cash price, and she obtained a mortgage for 20 years at 7%. What's Shelley's monthly payment?

Answer 1

To solve this we are going to use the loan payment formula: $P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} }$
where
$P$ is the payment
$PV$ is the present debt
$r$ is the interest rate in decimal form 
$n$ is the number of payments per year 
$t$ is the time in years 

Since she paid 20% of the value of the home, $PV=204000-(240000)20$%=163200
Now, to convert the interest rate to decimal form, we are going to divide the rate by 100% $r= \frac{7}{100} =0.07$. Since we are finding Shelly's monthly payment and a year has twelve months, $n=12$. We also know that $t=20$, so lets replace those values in our formula:
$P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} }$
$P= \frac{ \frac{0.07}{12}(163200)}{1-(1+ \frac{0.07}{12})^{-(12)(20)} }$
$P=1265.29$

We can conclude that Shelly's monthly payment is $1265.29