Amortization Schedules: Principal and Interest Breakdown
Master loan amortization schedules and payment breakdowns for Exam FM.
Level Payment Amortization
When a loan of L is repaid with n level payments of R at interest rate i, R = L / a-angle-n. Each payment is split into interest and principal: the interest portion of payment t is I_t = i * B_{t-1}, where B_{t-1} is the outstanding balance after payment t-1. The principal portion is P_t = R - I_t. The outstanding balance after payment t is B_t = B_{t-1} - P_t.
Prospective formula: B_t = R * a-angle-(n-t). Retrospective formula: B_t = L*(1+i)^t - R*s-angle-t. Both give the same answer and either may be more convenient depending on the problem.
Key Relationships
In a level-payment amortization: P_t = R * v^(n-t+1), so the principal portions form a geometric sequence increasing by factor (1+i). The interest portions decrease correspondingly. The sum of all principal portions equals L, and the sum of all interest portions equals n*R - L (total interest paid).
These formulas mean you can find the principal and interest in any specific payment without building the entire schedule. For example, P_1 = R * v^n and P_n = R * v.
Exam FM Applications
Exam FM problems may ask for: the outstanding balance at a specific time, the interest or principal portion of a specific payment, the total interest paid over a range of payments, or how the schedule changes with a rate adjustment. For total principal paid from payment j+1 to payment k: sum = B_j - B_k = R * (a-angle-(n-j) - a-angle-(n-k)). For total interest: sum of interest portions = (k-j)*R - (B_j - B_k). Practice these calculations until they are automatic.