**Payments on a Balloon Loan = [PV – {balloon amount ÷ (1 + r) ^{n}} ] × [ r ÷ {1 – (1 + r)^{-n} } ]**

P = Payment

PV = Present Value

r = rate per period

n = number of periods

Balloon loan payment formula focuses on the amount one will need to pay on a loan with pending balance after all premiums are paid. Typically, balloon loan payment approach can be seen at auto leases, some personal loan types and balloon mortgages also.

Balloon loans basically are such types of loan where a remaining balance is left after each periodic payment is cleared in full. The balloon loan payment formula can also be used to calculate any type of annuity where balance is remaining after all periodic payments are fulfilled. Annuity is basically a series of periodic payments, __Annuity payment formula__ is most commonly used to calculate payments on it. However, balloon loan payment equation can also be utilized lets go through an example;

Mr. Stewart has an interest bearing account with $10,000 in his account at the end of 2^{nd} year he is aiming to have a remaining balance of $4,500. The monthly amount which he withdraws can be calculated using the balloon loan payment formula.

A common person who don’t know much depth about annuity and difference between __compound interest__ and __simple interest__ will simply estimate things by subtracting principal amount and ending balance to determine the withdrawal amount. Although this approach is quick and works best for rough estimates however it do not give exact figures to calculate periodic payments or withdrawals.

## Balloon loan payment formula example

Lets suppose that Miss. Isabel lives in California and takes a loan for $9,500 and it will finance her for 3 years with ending balloon balance of $2,500 and rate will be 12% per annum. The principal loan amount is basically the present value of loan, here in the equation ** n** will be 36 (months) and

**will be 1% (per month rate).**

*r*Payments on a Balloon Loan = [$9,500 – {$2,500 ÷ (1 + 0.01)^{36}} ] × [ 0.01 ÷ {1 – (1 + 0.01)^{-36} } ]

This result in a payment of $257.50 each month which will due after one month and last payment will be paid at the end of loan. The remaining balance after the end of loan term will be a balloon balance and it will be $2,500 after 36 months.

Although the calculations in real life are carried out in different ways and actual payments and balloon balance differs due a number of involving factors including due dates, late penalties, rounding fees and compounding approaches. So, we do not claim any responsibilities for that, this formula is for educational purposes only.

### Deriving of balloon loan payment formula

Basically, balloon loan payment formula is derived by using two different forms of equations the first part calculates ‘PV of periodic payments’ while the second part calculates ‘Annuity payment factor’.

Payments on a Balloon Loan = [PV – {balloon amount ÷ (1 + r)^{n}} ] × [ r ÷ {1 – (1 + r)^{-n} } ]

In the above it can be seen equation that the 2^{nd} part of formula is basically an annuity payment factor. Moreover, this equation is commonly used to calculate payment on an annuity. While you may know that an annuity is a series of periodic payments which must not be confused with financial instruments. To calculate the annuity of a cash flow, the original balance is multiplied with annuity payment factor.

While on the other side 1^{st} portion of the formula focuses on calculating the present value of the payments. The balloon payment is discounted to its present value and then subtracted from the 2^{nd} part of equation. This calculation gives the amount of original balance on the loan at the end which is also known as balloon payment.