Question

The cost of a truck is $18,000 and am approved for an 8% loan but can choose to finance the loan for either 48 or 60 months.

What will be the additional cost over the life of the loan, if i choose the 60 month term instead of 48 months? can you please give a formula that is clear?

Answer 1

Step 1: First find the monthly payment using Present Value of Annuity(PVA) formula for both 48 month term and 60 month term:

Step 2: Multiply the monthly payment with total number of payments ( i.e 48 and 60) which will give you total amount you will be paying if you choose that option.

Step 3 : Difference in both amount found in Step 2 will be the additional cost if you choose 60 month term.

Solution:

Formula is:

Where,
PVA = Present Value of Annuity
A = Annuity or monthly payment
i = rate of interest
n = number of years
a = number of payments per year
na = number of payments or total months

First let us find monthly payment if we choose 48 months option.

Therefore, monthly payment for 48 month term will be $439.43

So total amount paid in 48 months will be $439.43 * 48 = $21,092.64......................................(1)

Now let us solve with the second option i.e 60 month plan

Therefore, Monthly payment for 60 month plan will be $364.98

Total amount paid in 60 months will be $364.98 * 60 = $21,898.51 ..................................(2)

So additional cost of choosing 60 month term plan over 48 is

= $21,898.51 - $21,092.64

= $805.74