Amortization

Explanation

Most mortgages, car loans and student loans are amortizing: you pay the same amount every month, and by the final payment the balance is zero. Each payment first covers the interest that built up that month on the remaining balance; whatever is left over reduces principal.

Because the balance is largest at the start, interest takes most of the early payments. As principal falls, interest shrinks and more of each payment goes to principal. That is why extra payments early in a loan save the most interest.

The loan payment formula is the present value of an annuity solved for the payment: the loan amount equals the present value of all future payments at the loan’s rate.

In scenarios, loans you enter are amortized month by month so the app can track your remaining balance and interest paid. (The “amortization” method for 72(t) withdrawals uses the same formula, applied to a retirement balance instead of a loan.) Margin loans and SBLOCs are usually not amortizing: they are interest-only lines with no fixed payoff date.

Example

A $400,000 mortgage at 6.5% for 30 years. Monthly rate r = 0.065 ÷ 12 = 0.0054167; n = 360.

• PMT = $400,000 × 0.0054167 ÷ (1 − 1.0054167^−360) ≈ $2,528.27 a month

First payment:

• Interest: $400,000 × 0.0054167 = $2,166.67
• Principal: $2,528.27 − $2,166.67 = $361.60
• New balance: $399,638.40

After 10 years (120 payments) the balance is still about $339,105, even though you have paid about $303,393. Over the full 30 years you pay $2,528.27 × 360 = $910,178, of which $510,178 is interest.