I've been struggling for hours now with understanding a Topcoder problem,
Autoloan , but i cannot grasp the way of computing it from a mathematical point of view. The excerpt goes as follows:
A typical auto loan is calculated using a fixed interest rate, and is set up so that you make the same monthly payment for a set period of time in order to fully pay off the balance. The balance of your loan starts out as the sticker price of the car. Each month, the monthly interest is added to your balance, and the amount of your payment is subtracted from your balance. (The payment is subtracted after the interest is added.) The monthly interest rate is 1/12 of the yearly interest rate. Thus, if your annual percentage rate is 12%, then 1% of the remaining balance would be charged as interest each month. You have been checking out some of the cars at your local dealership, TopAuto. An excited salesman has just approached you, shouting about how you can have the car you are looking at for a payment of only monthlyPayment for only loanTerm months! You are to return a double indicating the annual percentage rate of the loan, assuming that the initial balance of the loan is price. I am given the price, the monthlyPayment, and the loanTerm.
Which is the mathematical way of computing this? What is the dependency between the monthlyPayment and the loanTerm? How do we compute this type of fixed rates?
All i understood is that each month, the interest will be computed taking into consideration the amount of debt left?
Thanks in advance!
Hint:
Check out the Khan academy video on computing compound interest; hopefully that sets you in the right direction.