Question

You borrow $395,000 to buy a home using a 15-year mortgage with an interest rate of 3.75 percent and monthly payment. What percentage of the total amount paid in the first 3 years will go toward interest?

Group of answer choices

60.3 percent

39.7 percent

68.4 percent

31.6 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   =3.75%/12 =0.3125%
	N= Number of periods =12*15 =180
	= [ $395000x0.003125 x (1+0.003125)^180]/[(1+0.003125)^180 -1]
	= [ $1234.375( 1.003125 )^180] / [(1.003125 )^180 -1
	=$2872.53
Step 2 :	Loan balance after 3 years
	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
	= $2872.5236[ 1-(1+0.003125)^-144 /0.003125]
	= $2872.53[ 1-(1.003125)^-144 /0.003125]
	= $2872.53[ (0.3619) ] /0.003125
	= $3,32,684.13
Step 3 :	Loan repaid = 395000-332684.13
	=$62315.87
	Total paymanet = $2872.53*12*3
	=103411.1
	Interest paid = $103411.1-62315.87
	=$41095.23
	% of interest paid = $41095.23/103411.1
	=39.7 percent