Question

Let’s say that we have a 20-year mortgage with an original loan balance of $150,000 at 7% interest per year. How much money (i.e., balance) do you still owe after the 7th year of the loan? (The loan is compounded monthly)

.	1. $129,385
	2.	Cannot be determined
	3.	$118,902
	4.	$133,722

Answer 1

Step 1 :	Calculation of 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   =7%/12 =0.5833333%
	N= Number of periods =20*12 =240
	= [ $150000x0.0058333333 x (1+0.0058333333)^240]/[(1+0.0058333333)^240 -1]
	= [ $874.999995( 1.0058333333 )^240] / [(1.0058333333 )^240 -1
	=$1162.95
Step 2 :	Calculation of loan balance after 7 years payment
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period =7%/12 =0.583333%
	n=number of period =(20-7) *12 = 156
	= $1162.95[ 1-(1+0.00583333)^-156 /0.00583333]
	= $1162.95[ 1-(1.00583333)^-156 /0.00583333]
	= $1162.95[ (0.5964) ] /0.00583333
	= $1,18,902.06
\	Correct Answer = $118902
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