Question

A home is bought for $420,000 with a 20% down payment.  The interest rate is 3.2% and the term is 30 years (paid monthly).  What is the monthly payment?

Answer 1

Price of home bought = $420,000 Down payment = 20% of $420,000 = 0.20 * $420,000 = $84000

Loan Amount = Price of home bought - Down payment = $420,000 - $84000 = $336,000

We know that for monthly payments on the loan we have to use the formula for PMT:

PMT = [P x R x (1+R)^N]/[{(1+R)^N}-1]

Here P is the Principal Loan Amount, R is the Rate of Interest and N is the Tenure or the loan

P = $336,000 R =3.2% = 3.2%/12 = 0.2667% N = 30years * 12 = 360 Months

PMT =  [$336,000 x0.2667% x (1+ 0.2666%)³⁶⁰ ]/[ (1+ 0.2666%)³⁶⁰ -1]

PMT =  [$336,000 x0.002667 x (1+ 0.002667 )³⁶⁰ ]/[ (1+ 0.002667 )³⁶⁰ -1]

PMT =  [$336,000 x0.002667 x (1.002667 )³⁶⁰ ]/[ (1.002667 )³⁶⁰ -1]

PMT =  [$336,000 x0.002667 x 2.60836 ]/[ 2.60836-1]

PMT =  $2337.3827 / 1.60836

PMT = $1453.27

Monthly payment is $1453.27.