Level-payment instruments: mortgages and amortizing loans

In short

• Level-payment instruments pay the same amount A every period until maturity: mortgages, amortizing loans and annuities.
• Find A by setting the PV of the payments equal to the principal: $A = \frac{r \times PV}{1-(1+r)^{-t}}$.
• Interest each period = outstanding balance × periodic rate. Principal repaid = A − interest.
• Over time the interest share falls and the principal share rises, although A never changes.
• The outstanding balance at any date = PV of the payments still to come.
• Monthly loans: annual rate ÷ 12, years × 12.
• Compounding forward gives the future value of level payments, $A[(1+r)^t - 1]/r$; payments at the start of each period (annuity due) are worth (1 + r) times more.