Loan Repayment Methods: Level Payment and Non-Level

Level Payment Loans

The most common repayment structure is level payments, where the borrower pays a constant amount R each period. For a loan of L repaid over n periods at rate i: R = L / a-angle-n. Early payments are mostly interest; later payments are mostly principal. The outstanding balance, interest, and principal in any period can be found using the amortization formulas.

A variation is level principal repayment, where the principal portion is constant at L/n each period and the total payment decreases over time as the outstanding balance (and thus interest) falls.

Non-Level Payments

Exam FM tests several non-level structures. Payments that increase arithmetically (by a constant amount each period) are handled with increasing annuity formulas. Payments that increase geometrically (by a constant percentage) use the geometric annuity formula. Balloon payments involve level payments for n-1 periods with a larger final payment. Drop payments have a smaller final payment.

For any repayment schedule, the fundamental principle is the same: the present value of all payments at the loan rate must equal the loan amount.

Refinancing and Rate Changes

When a loan is refinanced at a new rate, compute the outstanding balance at the refinancing date using the original terms, then use that balance as a new loan at the new rate. On Exam FM, refinancing problems may also involve fees or penalties. If the loan rate changes at a specified time (adjustable rate), recompute the payment for the remaining term using the outstanding balance and new rate. The outstanding balance at the changeover point is the same regardless of whether you use the prospective or retrospective formula.