Word Problem

Question

A dealership loans Tito $17,500 to buy a car with a 5.5% interest rate compounded monthly. if the length of the loan is 4 years, how much will Tito be charged for the car? 

Answer 1

Assuming the buyer will make monthly payments on the loan, you have to find the monthly payment of an annuity where

 

PV = $17500

FV = 0

i% = 5.5/12 = .4583

N = 48 months

PMT = ?

 

A financial calculator solves this easily or you can use a spreadsheet function. Using a formula is more complicated.

 

PMT = $406.99

 

Now you can multiply $406.99 by 48 to find the total amount to be paid: $19,535.44.

 

If there are no monthly payments but the buyer simply returns the money plus interest at the end of four years, then you have to find the future value of the loan which is

 

 

PV = $17500
FV = ?
i% = 5.5/12 = .4583
N = 48 months
PMT = 0

 

And the calculator solves for the future value which is $21,795.39

It is unlikely that a car dealer would make a term loan like this, without monthly payments.

Answer 2

We can use the equation A = P(1+r/n)^(nt)

 

P = 175000

 

r = .055

 

n = 12

 

t = 4

 

So we can just plug all values into the above formula to calculate:

 

A = 175000(1+.055/12)^(48)

 

The car delearship would be charging $21795.38