Question

You are considering taking out a loan of $11,000.00 that will be paid back over 12 years with quarterly payments. If the interest rate is 5.7% compounded quarterly, what would the unpaid balance be immediately after the thirteenth payment?

Answer 1

Step 1 :	Quarterly payment
	= [P x R x (1+R)^N]/[(1+R)^N-1]
	Where,
	P= Loan Amount
	R= Interest rate per period =5.7%/4 =1.425%
	N= Number of periods 12*4 =48
	= [ $11000x0.01425 x (1+0.01425)^48]/[(1+0.01425)^48 -1]
	= [ $156.75( 1.01425 )^48] / [(1.01425 )^48 -1
	=$317.97
Step 2 :	Loan balance after 13th 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
	= $317.9748[ 1-(1+0.01425)^-35 /0.01425]
	= $317.9748[ 1-(1.01425)^-35 /0.01425]
	= $317.9748[ (0.3906) ] /0.01425
	= $8,715.17