You are looking to buy a car. You can afford $440 in monthly payments for four years. In addition to the loan, you can make a $1,100 down payment. If interest rates are 7.25 percent APR, what price of car can you afford (loan plus down payment) ? (Do not round intermediate calculations and round your final answer to 2 decimal places.).

You can afford a car worth $29,399.05

Explanation:

Step 1

Determine the present value of the car using the expression below;

Present value=total monthly payments+down payment

where;

total monthly payments=monthly payments+number of months

monthly payments=$440

number of months in 4 years=4*12=48 months

replacing;

total monthly payments = (440*48) = $21,120

total monthly payments in 4 years=$21,120

down payment=$1,100

replacing;

Present value = (1,100+21,120) = $22,220

Step 2

Determine the future value by the expression below;

F. V=P. V (1+r) ^n

where;

F. V=future value

P. V=present value=$22,220

r=annual interest rate=7.25%=7.25/100=0.0725

n=4 years

replacing;

F. V=22,220 (1+0.0725) ^4

F. V=22,220 (1.0725) ^4

F. V=$29,399.05

You can afford a car worth $29,399.05