Question

You borrow $396,000 to buy a home using a 15-year mortgage with an interest rate of 3.00 percent and monthly payment. What percentage of the total amount paid in the first 5 years will go toward principal repayment?

Group of answer choices

58.2 percent

68.7 percent

31.3 percent

41.8 percent

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
	N= Number of periods
	= [ $396000x0.0025 x (1+0.0025)^180]/[(1+0.0025)^180 -1]
	= [ $990( 1.0025 )^180] / [(1.0025 )^180 -1
	=$2734.7
Step 2 :	Loan balance after 5th year
	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
	= $2734.7[ 1-(1+0.0025)^-120 /0.0025]
	= $2734.7[ 1-(1.0025)^-120 /0.0025]
	= $2734.7[ (0.2589) ] /0.0025
	= $2,83,210.33
Step 3 :	Principal repaid =n $396000-283210.33
	=$112789.7
	Total payment = $2734.7*12*5
	=$164082
	% of principal = 112789/164082
	=68.7 percent