You want to purchase a house, and you have agreed on a selling price of $230,000. The bank will give you a loan for 30 years, and the interest rate will be 3.5%. Assume that you will finance the entire amount. What is the remaining principal balance after one year (12 payments)? 

$225,585.40

Step-by-step explanation

The outstanding principal at every point in time is the present value of the remaining monthly payments, hence, the remaining principal balance after one year is the present value of the remaining monthly payments for 29 years.

The monthly payment can be determined using the formula below:

PV=monthly payment*(1-(1+r)^-n/r

PV(remaining principal balance for 30 years)=$230,000

r=monthly interest rate=3.5%/12=0.002916667( I chose 9 decimal places so as to achieve accuracy)

n=number of monthly payments in 30 years=30*12=360

$230,0000=monthly payment*(1-(1+0.002916667)^-360/0.002916667

$230,0000=monthly payment*(1-(1.002916667)^-360/0.002916667

$230,0000=monthly payment*(1-0.350472919)/0.002916667

$230,0000=monthly payment*0.649527081/0.002916667

monthly payment=$230,000*0.002916667/0.649527081

monthly payment=$1,032.80

We need to determine the present value of monthly payments for the remaining 29 years using the formula above, excel PV function or financial calculator approach.

Since, we have already made use of the formula approach above, let us explore the other two approaches now:

=-pv(rate,nper,pmt,fv)

rate3.5%/12

nper=number of monthly payments in 29years=29*12=348

pmt=1032.80(monthly payment)

fv=0(the balance after all monthly payments would be zero)

=-pv(3.5%/12,348,1032.80,0)

pv=$225,585.40

The financial calculator would be set to its default end mode before making the following inputs:

N=348(same nper above)

PMT=1032.80

I/Y=3.5%/12

FV=0

CPT PV=$225,585.40