SOLUTION: PLZZ help!!!!!!!!!!!!!!!!!!!! A young couple that recently had their third child decide they need to purchase a new van. They make a down payment of $10,000 and finance the rema

Algebra ->  Finance -> SOLUTION: PLZZ help!!!!!!!!!!!!!!!!!!!! A young couple that recently had their third child decide they need to purchase a new van. They make a down payment of $10,000 and finance the rema      Log On


   

Question 585415: PLZZ help!!!!!!!!!!!!!!!!!!!!
A young couple that recently had their third child decide they need to purchase a new van. They make a down payment of $10,000 and finance the remaining $22,000 to purchase a 2010 Toyota Sienna. They arrange financing with their local financial institution and arrange an annual interest rate of 5.2% compounded monthly. They decide to make monthly payments of $400. What will be the outstanding balance on their loan after 24 months?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

L = 22,000 - 10,000 = 12,000 is the loan amount
i = r/12 = 0.052/12 is the monthly interest rate
n = 24 is the number of months
P = 400 is the monthly payment

B(n) = L*(1+i)^n - P*( (1+i)^n - 1 )/i
B(24) = 12000*(1+0.052/12)^24 - 400*( (1+0.052/12)^24 - 1 )/(0.052/12)
B(24) = 3,218.25965151418
B(24) = 3,218.26

Answer: $3,218.26

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More Info about the formula used:
http://financeformulas.net/Remaining_Balance_Formula.html

Here is a table of the balances

The idea is that you compute the compound interest first and then the payment is made afterward.
This process is repeated 24 times to generate the 24 rows.