What is Reverse Amortization?
Reverse amortization, often known as negative amortization, occurs when the monthly payments on a loan are not enough to cover the interest due. Instead of the balance decreasing over time, the unpaid interest is added to the principal, causing the loan balance to grow. This is a critical concept for US citizens considering reverse mortgages or certain student loan deferment plans.
The Mathematics of Balance Growth
The calculation relies on compounding interest where the principal increases each period. The formula for the balance after one period ($B_{new}$) is:
Bnew = Bold + (Bold × r) - P
- r: Monthly Interest Rate (Annual Rate / 12)
- P: Periodic Payment (if any)
Step-by-Step Example
If you have a $100,000 balance at a 6% interest rate with no monthly payments:
- Month 1: Interest is $500 ($100,000 × 0.005). New balance becomes $100,500.
- Month 2: Interest is $502.50 ($100,500 × 0.005). New balance becomes $101,002.50.
Notice how the interest grows each month because it is being calculated on a larger and larger balance. This "interest on interest" effect is what defines reverse amortization scenarios.