Question

Joseph is considering a used car currently valued at $12,000. He can get an interest rate of 2.5% annually for a 5 year car loan. Joseph currently has $14,000 in a savings account and wants to use some of his savings for a down payment. If Joseph decided to put $3,000 down as a down payment, what are his monthly payments? If Joseph decided to put $5,000 down as a down payment, what are his monthly payments? How much does Joseph save in interest if he puts $5,000 down compared to $3,000? If Joseph decides to pay for the whole thing what could he potentially save in interest payments? If Joseph can invest $12,000 in an 8% annual investment. Alternatively he is considering just paying cash for the car leaving him no payment. Which would you recommend and why? Include the numbers!!

Answer 1

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Value of Car	12,000.00
Rate of Interest	2.50%
Period (Years)	5.00
Down payment	3,000.00			Down payment	5,000.00
Loan Value	9,000.00			Loan Value	7,000.00
We Know,				We Know,
Monthly Payment=	PV*i			Monthly Payment=	PV*i
	1-(1+i)^-n				1-(1+i)^-n
PV	Loan Value	9,000.00		PV	Loan Value	7,000.00
Instalments in a year		12.00		Instalments in a year		12.00
n	12*5	60.00		n	12*5	60.00
i	2.5%/12	0.21%	0.00208333333333333	i	2.5%/12	0.21%	0.00208333333333333
Monthly Payment=	9000*0.00208333333333333			Monthly Payment=	7000*0.00208333333333333
	1-(1+0.00208333333333333)^-60				1-(1+0.00208333333333333)^-60
Monthly Payment=	18.75			Monthly Payment=	14.58333333
	1-(1.00208333333333333)^-60				1-(1.00208333333333333)^-60
Monthly Payment=	18.75			Monthly Payment=	14.58333333
	1-0.882611659150112				1-0.882611659150112
Monthly Payment=	18.75			Monthly Payment=	14.58333333
	0.11738834				0.117388341
Monthly Payment ($)	159.73			Monthly Payment ($)	124.23
Total payments	9,583.58	159.73*60		Total payments	7,453.89	124.73*60
Loan Value	9,000.00			Loan Value	7,000.00
Interest paid	583.58			Interest paid	453.89
Difference in Interest paid		129.68
Joseph will save $ 129.68 in interest if he puts $5,000 down compared to $3,000.
If Joseph decides to pay for the whole thing he could have saved $ 453.89 in interest payments.
If Joseph can invest $12,000 in an 8% annual investment.
P	12,000.00
i	8%	0.08
Years	5.00
Interest amount	P*((1+i)^n-1)
Interest amount	12000*((1+.08)^5-1)
Interest amount	5,631.94
Its better to take loan against car because Joseph can invest $ 12,000 which will earn him interest of $ 5,631.94.
It is much more than the total interest he has to pay on loan.