Data Source and Methodology
Payments follow the level-payment amortization formula used in Truth in Lending (Regulation Z) Appendix J. The lump-sum prepayment reduces the balance at the payment number you choose. After the lump is applied, the calculator keeps the scheduled payment unchanged and simulates the loan month by month until it pays off to compute interest savings and months eliminated.
Formulas Used
Monthly rate: \( r = \dfrac{\text{APR}}{12} \)
Scheduled payment: \( M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}} \) (if \( r = 0 \) then \( M = P/n \))
After a lump sum \( L_{\text{ump}} \) at payment \( k \):
Remaining balance \( B_k = B_{k-1} - (M - B_{k-1} \cdot r) - L_{\text{ump}} \)
Monthly interest is recalculated each period as \( B_t \cdot r \) until the balance reaches zero.
Frequently Asked Questions
Will my lender reduce the required payment?
Usually no. After a lump sum you keep making the same payment and the term shortens. Some lenders allow a “recast” if you request it.
How do I choose the payment number?
Payment #1 applies the lump sum immediately. Larger payment numbers simulate applying the lump later in the loan, which saves less interest.
Do I have to pay extra every month?
No. This tool models a single lump sum while keeping the regular payment the same.