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

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.