Question

A mortgage of $100,000 is amortized over 25 years using level payments at the end of each quarter and the first interest payment at the end of the first quarter is $2411.37. Calculate the 62nd principal payment amount.

a. 1074.21

b. 1048.92

c. 1100.11

d. 1024.22

e. None of these answers

Answer 1

Correct Answer b. 1048.92
Step 1 :	Calcuation of interest rate per quarter
	=$2411.37/100000
	2.4114%
Step 2:	Calculation of Montly 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
	N= Number of periods
	= [ $100000x0.0241137 x (1+0.0241137)^100]/[(1+0.0241137)^100 -1]
	= [ $2411.37( 1.0241137 )^100] / [(1.0241137 )^100 -1
	=$2656.56
Step 3:	Calculation of balance of laon after 61st payment
	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
	= $2656.56[ 1-(1+0.0241137)^-39 /0.0241137]
	= $2656.56[ 1-(1.0241137)^-39 /0.0241137]
	= $2656.56[ (0.6052) ] /0.0241137
	= $66,669.31
Step 4:	Calculation of balance of laon after 62st payment
	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
	= $2656.56[ 1-(1+0.0241137)^-38 /0.0241137]
	= $2656.56[ 1-(1.0241137)^-38 /0.0241137]
	= $2656.56[ (0.5956) ] /0.0241137
	= $65,620.40
Step 5:	Calculation of principal paid
	=$66669.31-65620.40
	=$1048.92