Question

You purchased a new house for $200,000 and financed the entire purchase with a $200,000 mortgage, payable monthly over 30 years at a yearly rate of 5.5%. How much do you owe on this house today after making 4 years of monthly payments?

Answer 1

Step 1:	Monthly payment
	EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
	Where,
	EMI= Equal Monthly Payment
	P= Loan Amount
	R= Interest rate per period   =5.5%/12 =0.4583333%
	N= Number of periods =30*12 =360
	= [ $200000x0.004583333 x (1+0.004583333)^360]/[(1+0.004583333)^360 -1]
	= [ $916.6666( 1.004583333 )^360] / [(1.004583333 )^360 -1
	=$1135.58
Step 2:	Loan amount after 4 years monthly payment done
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $1135.58[ 1-(1+0.0045833333)^-312 /0.0045833333]
	= $1135.58[ 1-(1.0045833333)^-312 /0.0045833333]
	= $1135.58[ (0.7599) ] /0.0045833333
	= $188,277
	Correct Answer =$188277