Question

You want to buy a $224,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan at 5.3% interest for the rest.What is the monthly payment?

Answer 1

Step-by-step explanation

We are simply asked to obtain the monthly payment on the house loan

To do this, we will make use of the formula to compute the equal monthly payment (EMI)

`\begin{gathered} The\text{ principal here will be:} \\ (100-20)\text{ \% }*$ \text{ \$}224,000 $ \end{gathered}`
`P=0.8*224,000=\text{ \$179200}`

Next, we know that there are 12 months in a year

In 30 years, there will be

`30*12=360\text{ months}`

This means that

`n=360`
`\begin{gathered} r=\frac{5.3\text{ \%}}{12} \\ \\ r=(0.053)/(12) \\ \\ r=0.00441 \\ \end{gathered}`

We can now substitute the values above to get EMI

`EMI=179200*(0.00441(1+0.00441)^(360))/((1+0.00441)^(360)-1)`

Simplifying further

`EMI=\text{ \$994.216}`

Hence, the monthly payment is $994.22