Advanced Financial Mathematics – Reducing Balance Loans (Part 1)

Vocabulary flashcards summarising the essential terms and definitions related to modelling and analysing reducing balance loans, amortisation tables, and the use of finance solver technology.

Reducing Balance Loan

A loan repaid with regular instalments in which the outstanding balance decreases over time as interest is added and a fixed payment is subtracted each period.

Amortisation

The process of gradually repaying a debt through scheduled, periodic payments of principal and interest until the balance reaches zero.

Amortisation Table

A step-by-step schedule showing each payment, the portion applied to interest, the principal reduction, and the remaining balance of a loan.

First-Order Linear Recurrence Relation

An equation of the form V₀ = initial value, V{n+1} = aVn − b that models how a loan balance changes each period through interest (a) and fixed payment (b).

Principal

The original amount borrowed or the unpaid portion of the loan on which interest is calculated.

Principal Reduction

The part of a payment that lowers the outstanding loan balance (payment minus interest for that period).

Interest (Loan Context)

The cost of borrowing money, calculated as a percentage of the outstanding principal for each compounding period.

Annual Interest Rate

The percentage of the principal paid as interest over one year; equals periodic rate × number of compounding periods per year.

Periodic Interest Rate

The interest rate applied each compounding period; equals annual rate divided by number of periods per year.

Payment (Pmt)

The fixed amount paid at regular intervals toward a loan’s principal and interest.

Balance (Loan)

The amount still owed on a loan after accounting for all previous principal reductions.

Total Interest Paid

The sum of all interest amounts over the life of the loan; calculated as total payments made minus the initial principal.

Present Value (PV)

The current value of a loan or investment; for loans, the amount borrowed (entered as positive in a finance solver).

Future Value (FV)

The value remaining after the final period; for a fully repaid loan, FV = 0.

Total Number of Periods (N)

The total count of repayment intervals over the life of the loan (e.g., months in a 25-year monthly loan).

Payment Periods per Year (P/Y)

The number of times payments are made in one year (e.g., 12 for monthly).

Compounding Periods per Year (C/Y)

The frequency with which interest is added to the balance in one year; often equal to P/Y for reducing balance loans.

Finance Solver

Calculator or software feature that computes unknown loan variables (e.g., payment, balance, periods) given PV, FV, interest rate, and frequency inputs.

Loan Amortisation Formula

Mathematical expression or recurrence relation used to determine payment, interest, or balance details of a reducing balance loan.

Impact of Interest-Rate Change

Effect on repayment amount, total interest, and loan duration when the annual interest rate increases or decreases.

Mortgage

A long-term reducing balance loan secured by real estate, typically repaid monthly over 15–30 years.

Total Cost of Loan

The sum of all payments made over the loan term; equals initial principal plus total interest paid.