Question

lars has been approved for$420,000, 20-year mortgage with an APR of 5.125%.What is his monthly payment ? How much interest would he expect to pay on the loan in one month?How much of the monthly payment will go towards the principal?

Answer 1

Monthly Payment = $2,286.85

Interest on first month payment = $1,793.75

Principal value on first month payment = $493.10

Explanation:

lars has been approved for $420,000 for loan.

Time for loan = 20-years

APR (Annual Rate of interest ) = 5.125%

We need to find monthly payment. First month interest and First month principle.

Formula for loan:

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

Where,

p is monthly payment.

PV = Loan Amount (PV=$420,000)

R = Rate of interest (R=0.05125)

t = Loan period ( t=30)

n = Mode of payment (n=12)

Substitute the value into formula and solve for p

`p=(420000\cdot (0.05125)/(12))/(1-(1+(0.05125)/(12))^(-12\cdot 30))`

p=$2,286.85

Thus, Monthly Payment =$2,286.85

Interest for first month
`=420000* (0.05125)/(12)=1793.75`

Interest pay on the loan in on month = $1,793.75

Principle value on first month payment = 2286.85 - 1793.75 = $493.10

The monthly payment will go towards the principal is $493.10