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= ( (r)/(n)(PV))/(1-(1+ (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= (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= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )`

`P= ( (0.07)/(12)(163200))/(1-(1+ (0.07)/(12))^(-(12)(20)) )`

`P=1265.29`

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