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

Question

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.

@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, 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
There is a balloon loan example calculation with Excel equivalent here: https://money.stackexchange.com/a/106924/11768 and another example here: https://money.stackexchange.com/a/95784/11768 — Chris Degnen, Jun 30 '20 at 06:18

score 1 · Answer 1 · answered Jun 28 '20 at 22:45

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.

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

1 Answers1