Question

You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 9% APR based on end-of-month payments.

What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.
$  

What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent.
$  

Answer 1

Loan amount that can be borrowed that has monthly payment of $450 is: $18,083

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Principle	P	18,083.00
Rate of interest per period:
Annual rate of interest		9.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.09 /12 =	0.7500%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	4
Total number of payments	N	4*12 =	48
Period payment using the formula	=	[ 18083*0.0075*(1+0.0075)^48] / [(1+0.0075 ^48 -1]
Monthly payment	=	450.00

Using the cash in hand and loan, car that can be purchased is 22,083.

If tenure is 60 months, loan can be borrowed is 21,678. and car can be purchased is 25,678

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Principle	P	21,678.02
Rate of interest per period:
Annual rate of interest		9.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.09 /12 =	0.7500%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5*12 =	60
Period payment using the formula	=	[ 21678.02*0.0075*(1+0.0075)^60] / [(1+0.0075 ^60 -1]
Monthly payment	=	450.00