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I am looking into PCP finance for a car and I have found estimates where I enter a term and a deposit, and am given a monthly payment for the loan.

Some sites (BMW for example) will let you enter a target monthly payment and term, and they will provide the deposit required to achieve this target. I want to know how this figure can be calculated when the monthly payments, period, balloon payment, and term, are known figures.

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    ifsautoloans.com/car-loan-interest Subtract the balloon payment from the target price, and solve for the down payment. (Who said you'd never need algebra after high school?) – RonJohn Mar 13 '19 at 19:48
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    @BenMiller one line answers are frowned upon. – RonJohn Mar 13 '19 at 20:17
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    @RonJohn Yes, but so are answers in the comments. The solution to avoid posting a one-line answer is not to post it as a comment; instead, you could flesh out your answer a little, or wait until you have time to expand on it, or let someone else answer and then upvote that. Posting a short answer as an answer is better than posting an answer as a comment, for the reasons listed in the meta question. – Ben Miller - Remember Monica Mar 13 '19 at 20:20
  • @RonJohn If you add an answer with an example, I'd likely accept it – Adam Chance Mar 13 '19 at 20:27
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The standard formula for calculating loan payments is:

MathJax formula: $$P=L\frac{c(1+c)^n}{(1+c)^n-1}$$

where:

  • P = monthly payment
  • L = Loan amount
  • c = monthly interest rate. This is the annual interest rate divided by 12.
  • n = number of months in the loan (years * 12)

You want to choose a monthly payment, interest rate, and loan term and see how much you can borrow. If we solve for L, we get:

MathJax formula: $$L=P\frac{(1+c)^n-1}{c(1+c)^n}$$

Here is an example: Let's say that you want to pay $400 per month for 5 years, with a 4% interest rate. Plugging in P=400, c=0.04/12=0.0033, and n=5*12=60, you get a loan amount of $21,720.

Knowing that, if you want to buy a new 2020 BMW 2 Series sedan for $38,495, and you want a loan with these terms, you'll need to come up with a $16,775 down payment.

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