Question

Natalie has been offered the two choices to finance her new $35,000 car, and she needs help knowing which to take. One option is a 7.5%, 48-month loan, and the other option is a 4.5%, 36-month loan. Assume no down payment. Which of the following is true? Helpful tip: You will want to calculate and make note of the monthly payment and total cost of the loan for both financing options.

Answer 1

Step-by-step explanation:

To find out what Natalie would give as a monthly installment, we first need to calculate the monhly payment on a $35000 loan with 7.5% interest rate for 48 months using present value annuity formual.

PV = 35000

r= 7.5% = 7.5%/12 = 0.00625

t = 48

PMT = monthly payments

PMT = (r*PV) / [1 - (1+r)-n]

=( 0.00625* 35000) / [1-(1+0.00625)-48 ]

= 218.75 / [ 1 - (1.00625)-48 ]

= 218.75 / [ 1 - 0.74151 ]

= 218.75 / 0.25849

=$846.26

Monthly payment of $846.26

Total Cost = Monthly payment * 48

=$40620.56

For second loan option

r = 4.5%/12 = 0.00375

n = 36

PV = $35000

Using same formual

PMT = (r*PV) / [1 - (1+r)-n]

=( 0.00375* 35000) / [1-(1+0.00375)-36 ]

= 131.25 / [1 - (1.00375)-36 ]

= 131.25 / [ 1 - 0.873937 ]

= 131.25 / [ 0.126063

= $1041.42

Monthly payment of $1041.42

Total payment = 1041.42*36

= $37481.12

Thus, the 48 month or 4 year loan has monthly payment of $846.26 and total cost of $40620.56

And , the 36 month or 3 year loan has monthly payment of $1041.42 and total cost of $37481.12