Question

When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.

Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.

Suppose you are buying a new truck at a price of $19,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $1,900 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $17,100) at an APR of 5.5%.

What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)

Answer 1

Given,

Amount of loan(p) = $17100

Period of loan(n) = 2 years = 24 months

Annual percentage Rate (r)= 5.5%

Therefore, Equated Monthly Installment ( EMI) =

P × (r÷12) × {1+ (r÷12)}^n ÷ [{1 + (r÷12)}^n-1]

= p × (5.5%÷12)×{1+(5.5%÷12)}^24 ÷ [{1+(5.5%÷12)}^24-1]

= $17100 × .4583333% × {(1+ .004583333)^24} ÷ {(1 + .004583333)^24 - 1}

=$78.375 × { (1.004583333)^24} ÷ {(1.004583333)^24-1}

=$78.375 × 1.115998÷(1.115998-1)

=$78.375 × 1.115998 ÷ .115998

= $754.03

Therefore, monthly payment rounded off to nearest cent = $800