Question

A bank recently loaned you $14,015.00 to buy a car. The loan is for 4 years in is fully amortized. The nominal rate on the loan is 11%, and payments are made at the end of each month. What will be the remaining balance on the loan after you make payment number 25?

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 =11%/12 =0.9166667%
	N= Number of periods =12*4 =48
	= [ $14015x0.0091666667 x (1+0.0091666667)^48]/[(1+0.0091666667)^48 -1]
	= [ $128.4708338005( 1.0091666667 )^48] / [(1.0091666667 )^48 -1
	=$362.2249
Step 2 :	Calcualtion of loan amount after 25th payment
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period =11% /12 =0.916667%
	n=number of period =48-25 =23
	= $362.2249[ 1-(1+0.009166667)^-23 /0.009166667]
	= $362.2249[ 1-(1.009166667)^-23 /0.009166667]
	= $362.2249[ (0.1893) ] /0.009166667
	= $7,480.78