# Calculate the deposit on a loan when the monthly payment, interest rate, and balloon are known

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.

• 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
• – Ben Miller - Remember Monica Mar 13 '19 at 20:03
• @BenMiller one line answers are frowned upon. – RonJohn Mar 13 '19 at 20:17
• @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

The standard formula for calculating loan payments is:

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:

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.