Question

Garrett and Erin are borrowing $170,000 to purchase a new home. They have been approved for a 30-year loan with an interest rate of 5.75%. What will be their monthly payment?

Answer 1

$1,286.81

Explanation:

First off we need to solve for the total amount to be paid after 30 years with the interest rate.

We use the formula:

`A=P(1+rt)`

Let's break down the values that we have available.

P = 170,000

r = 5.75% or 0.0575

t = 30 years

Now we can solve for the total amount.

`A=P(1+rt)`

`A=170,000(1+0.0575(30))`

`A=170,000(1+1.725)`

`A=170,000(2.725)`

`A=463,250`

Now that we have the total amount to be paid after 30 years, we now can find out how much the monthly payment will be by dividing the total amount by the number of payments in month over 30 years.

30 year = 360 months

463,250 / 360 = $1,286.81

So Garrett and Erin need to pay a monthly fee of $1,286.81 over the next 30 years.

Answer 2

`\$ 992.074`

Explanation:

Since, the periodic payment of a loan,

`P=(r(P.V.))/(1-(1+r)^(-n))`

Where, P.V. is the principal amount,

r is the rate per period,

n is the number of periods,

Given,

P.V. = $ 170,000,

Annual rate = 5.75 % = 0.0575,

Thus, the rate per month,

`r=(0.0575)/(12)`

Also, time = 30 years,

So, the number of months in 30 years,

n = 360 ( 1 year =12 months )

Hence, the monthly payment of the loan is,

`P=((0.0575)/(12)(170000))/(1-(1+(0.0575)/(12))^(-360))`

`P=\$ 992.073855954\approx \$ 992.074`