Question

Derek borrows $299,744.00 to buy a house. He has a 30-year mortgage with a rate of 5.62%. After making 81.00 payments, how much does he owe on the mortgage?

Answer format: Currency: Round to: 2 decimal places.

Answer 1

Step 1 :	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   =5.62/12% =0.4683333%
	N= Number of periods =30*12 =360
	= [ $299744x0.0046833333 x (1+0.0046833333)^360]/[(1+0.0046833333)^360 -1]
	= [ $1403.8010566752( 1.0046833333 )^360] / [(1.0046833333 )^360 -1
	=$1724.54494
Step 2 :	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period =5.62%/12 =0.46833333%
	n=number of period =(30*12)-81 =279
	= $1724.54494[ 1-(1+0.0046833333)^-279 /0.0046833333]
	= $1724.54494[ 1-(1.0046833333)^-279 /0.0046833333]
	= $1724.54494[ (0.7284) ] /0.0046833333
	= $2,68,236.40