## Periodic Payment on a Balloon Note
The balloon loan payment formula is used to calculate the payments on a loan that has a balance remaining after all periodic payments are made. Examples of loans that may use the balloon loan payment formula would be auto leases, balloon mortgages, and any other form of loan not paid in full at its end date. Lenders often use this in conjunction with LTV ratios to assess risk.
The formula for a balloon loan payment could also be used for any form of annuity where a balance is left after all periodic cash flows are made. An annuity is simply a series of periodic payments.
## How is the Balloon Loan Payment Formula Derived?
The balloon loan payment formula can be found by first separating the two main parts of the formula: the annuity payment factor and the present value of the balloon amount.
### Annuity Payment Factor
This is the formula used to calculate the payment on any type of annuity. The payments or cash flows of an annuity can be found by multiplying the original balance or present value times the annuity payment factor.
### Discounting the Balloon Amount
The balloon amount is discounted to its present value in order to subtract it from the sum of the present value of the payments and balloon amount, which is the original balance on the loan.
## Example Case
Suppose that a loan is taken out for **$11,000** to be financed for **3 years** with a balloon balance of **$5,000** and a rate of **12% per year**.
The original loan amount of $11,000 is the Present Value (PV), 36 months is used for n, and 1% per month (12% per year) is used for r.
This would result in payments of **$249.29**.
It is important to remember that the actual payment and remaining balance in practice may vary depending on when payments are due, when payments are made, due to rounding, fees, compounding basis, and various other factors. This formula is only for educational purposes.
