Loan
Remaining balance after k payments
Grow the original principal forward k periods, then subtract the accumulated value of the payments made so far. This is how the interest/principal split is computed month by month.
The Formula
B = P(1 + r)^k - M x (((1 + r)^k - 1) / r)
Grow the original principal forward k periods, then subtract the accumulated value of the payments made so far. This is how the interest/principal split is computed month by month.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| k | Number of payments already made | count | Used to build an amortization schedule or to quote a payoff figure. |
What Each Symbol Means
kcount
Number of payments already made
Used to build an amortization schedule or to quote a payoff figure.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate loan payment page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Loan Payment, filed under Finance. Every number the guide produces comes from substituting into this one line.