value 1000 points You are looking to buy a car You can affor

value 10.00 points You are looking to buy a car You can afford $410 in monthly payments for four years. in addition to the loan, you can make a $1,400 down payment. If interest rates are 8 00 percent APR, what price of car can you afford? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Present value Hints References eBook & Resources Hit #1

Solution

EMI = $410

Time period (n)= 4 years = 48 months

Interest rate = 8% p.a.

Monthly interest rate (r) = 8/1,200

= 0.0067

Loan amount = P = ?

Loan amount can be calculated using the given below formula:

EMI = [ P x r x ( 1 + r )ⁿ ]/ [ ( 1 + r )ⁿ - 1 ]

410 = [ P x 0.0067 x ( 1 + 0.0067 )⁴⁸ ]/ [ ( 1 + 0.0067 )⁴⁸ - 1 ]

410 = [ P x 0.0067 x ( 1.0067 )⁴⁸ ]/ [ ( 1.0067 )⁴⁸ - 1 ]

410 = ( P x 0.0067 x 1.3775 )/ (1.3775 - 1)

410 = ( P x 0.0092 )/ 0.3775

P x 0.0092 = 410 x 0.3775

P = 154.775/0.0092

= $16,820 (approx.)

Hence, loan amount which can be afforded = $16,820

Down payment = $1,400

Hence, price of car = 1,400 + 16,820

= $18,220 (approx)