Question

A man has borrowed $10,000 which he will repay in 60 equal monthly installments. After his twenty-fifth payment he desires to pay the remainder of the loan at the time of the 26th payment in a single payment. At an interest rate of 2% per month what is the amount of the payment?

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
	N= Number of periods
	= [ $10000x0.02 x (1+0.02)^60]/[(1+0.02)^60 -1]
	= [ $200( 1.02 )^60] / [(1.02 )^60 -1
	=$287.68
Step 2 :	Loan due 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
	n=number of period
	= $287.6796[ 1-(1+0.02)^-35 /0.02]
	= $287.6796[ 1-(1.02)^-35 /0.02]
	= $287.6796[ (0.5) ] /0.02
	= $7,191.59
Step 3 :	Calculation of single payment
	=7191.59*1.02
	=$7335.42