Question

A woman purchased a new car today for $16,000. She paid $2,000 down and agreed to make 47 monthly installments of $250 and a nal balloon payment at the end of the 48th month. The interest rate is 15 percent compounded monthly. What is the amount of the final balloon payment?

Answer 1

Solution:
	Amount of the final balloon payment is $9,357.87
Working Notes:
	Car value today = down payment + Present value of annuity of $250 monthly payment of 47 months + Present value of 48th period balloon payment
	Present value of annuity of $250 monthly payment of 47 months
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	P=monthly payment=$250
	i= interest rate per period = 15%/12
	n= no. Of period = 47
	PV of annuity= Present value of annuity of $250 monthly payment of 47 months
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	present value of annuity= 250 x (1-1/(1+(15%/12))^47)/(15%/12)
	present value of annuity= $8,845.156105
	Car value today = down payment + Present value of annuity of $250 monthly payment of 47 months + Present value of 48th period balloon payment
	16,000 = 2,000 + $8,845.156105 + Present value of 48th period balloon payment
	Present value of 48th period balloon payment
	=16000 - 2000 - $8,845.156105
	=$5,154.843895
	Present value of 48th period balloon payment
	=Balloon payment/( 1 + (15%/12))^48
	=Balloon payment/( 1 + (15%/12))^48
	Present value of 48th period balloon payment = Balloon payment/( 1 + (15%/12))^48
	$5,154.843895 =   Balloon payment/( 1 + (15%/12))^48
	Balloon payment = $5,154.843895 x ( 1 + (15%/12))^48
	Balloon payment = $9357.870882
	Balloon payment = $9,357.87
	Car value today = down payment + Present value of annuity of $250 monthly payment of 47 months + Present value of 48th period balloon payment
	= 2000 + 250 x (1-1/(1+(15%/12))^47)/(15%/12) + $9357.870882/( 1 + (15%/12))^48
	=16,000
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