K, this should be right for ya... sorry if the format is somewhat elementary. I'm a sophmore in college, but this is my first helpful post on here.
"Suppose you want to buy a new car. You have $5000 in cash and can afford monthly payments of $250. a) What price car can you buy if you can obtain a 36-month loan and 6% compounded monthly? b) If you get the loan, what is the unpaid balance after 2 years? "
I actually remember deriving this equation once.. haha
Allright, THIS is your "Compounding Interest Equation". A is the total amount of money you have (that will be charged interest). ONLY MONEY that is assosciated with interest should go in this equation! Moving on... r is your interest rate, k is the number of times compounded per year, t is the time in years, and P is the amount before interest.
Your values are r=.06, k=12, t=3, and A= (250*36)=9000
Knowing to use A instead of P is the tricky part here, as well as knowing how to calculate it. Realize that you need to find how much money you have available AFTER the interest has accrued for 3 years!
So, we need to find out how much money (call it P) will equal $9000 after 36 months has gone by. This will allow us to spend every dollar when we add the $5000 cash we have NOW onto this number "P".
So, plug in you're numbers and solve for P (the Price of the car).
1+.06/12=1.005-> 1.005^36 = 1.19668 -> 9000/1.19668 = $7,520.804
Now, this means that $7,520.80 will come to a total of $9,000 after 36 months have passed by with monthly compounding at a 6% interest rate.
Since you have the $5,000 you started with and the $9,000 you will deposit over the next 3 years (which will really only be able to pay off $7520.80 towards the car since the rest will go to interest), you can buy a car worth:
$5,000 + $7520.80 = $12,520.80
I hope this makes sense.. it's my 'help' first post. Thanks is appeciated if it helped!