USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONS Vito Scaletta just bought his dream car,...

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USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREEQUESTIONS
Vito Scaletta just bought his dream car, 2019 Aston Martin DB9that cost $208,700. He paid $30,000 down and financed the balanceover 84 months at 6.25% p.a. (Assume that Vito makes all requiredpayments on time).
What will the balance on Vito’s loan be at the end of the fourthyear (that is, immediately after Vito makes his 48th payment on theloan)?

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4.1 Ratings (580 Votes)

Step-1:Calculation of monthly payment

Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$ 1,78,700	/	67.89554419
	=	$ 2,631.98

Working:

Loan amount	=	Cost of Car	-	Down payment
	=	$ 2,08,700	-	$ 30,000
	=	$ 1,78,700

Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.005208)^-84)/0.005208		i	6.25%/12	=	0.005208
	=	67.89554419		n		=	84

Step-2:Calculation of balance of loan at the end of fourth year

Loan balance is always present value of remaining monthly payment.

Loan balance	=	Monthly payment	x	Present value of annuity of 1
	=	$ 2,631.98	x	32.74913262
	=	$ 86,195.20

Working:

Present value of annuity of 1 for remaining time	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.005208)^-36)/0.005208		i	6.25%/12	=	0.005208
	=	32.74913262		n	84-48	=	36


So,
Balance on Vito’s loan will be at the end of the fourth year $ 86,195.20

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Transcribed Image Text

USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREEQUESTIONSVito Scaletta just bought his dream car, 2019 Aston Martin DB9that cost $208,700. He paid $30,000 down and financed the balanceover 84 months at 6.25% p.a. (Assume that Vito makes all requiredpayments on time).What will the balance on Vito’s loan be at the end of the fourthyear (that is, immediately after Vito makes his 48th payment on theloan)?