MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

To solve this we are going to use the loan payment formula: [tex]P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} } [/tex]

where

[tex]P[/tex] is the payment

[tex]PV[/tex] is the present debt

[tex]r[/tex] is the interest rate in decimal form

[tex]n[/tex] is the number of payments per year

[tex]t[/tex] is the time in years

Since she paid 20% of the value of the home, [tex]PV=204000-(240000)20[/tex]%=163200

Now, to convert the interest rate to decimal form, we are going to divide the rate by 100% [tex]r= \frac{7}{100} =0.07[/tex]. Since we are finding Shelly's monthly payment and a year has twelve months, [tex]n=12[/tex]. We also know that [tex]t=20[/tex], so lets replace those values in our formula:

[tex]P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} } [/tex]

[tex]P= \frac{ \frac{0.07}{12}(163200)}{1-(1+ \frac{0.07}{12})^{-(12)(20)} } [/tex]

[tex]P=1265.29[/tex]

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

where

[tex]P[/tex] is the payment

[tex]PV[/tex] is the present debt

[tex]r[/tex] is the interest rate in decimal form

[tex]n[/tex] is the number of payments per year

[tex]t[/tex] is the time in years

Since she paid 20% of the value of the home, [tex]PV=204000-(240000)20[/tex]%=163200

Now, to convert the interest rate to decimal form, we are going to divide the rate by 100% [tex]r= \frac{7}{100} =0.07[/tex]. Since we are finding Shelly's monthly payment and a year has twelve months, [tex]n=12[/tex]. We also know that [tex]t=20[/tex], so lets replace those values in our formula:

[tex]P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} } [/tex]

[tex]P= \frac{ \frac{0.07}{12}(163200)}{1-(1+ \frac{0.07}{12})^{-(12)(20)} } [/tex]

[tex]P=1265.29[/tex]

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