SL 1.7 — Amortization & Annuities Using Technology
| Key Term | Simple Description |
|---|---|
| Present Value (PV) | The value now (loan amount or lump-sum investment). |
| Payment (PMT) | Regular fixed amount paid or received every period. |
| Interest Rate (r) | Percentage charged or earned each period. |
| Number of Periods (n) | Total count of equal time intervals (months, years, etc.). |
| Future Value (FV) | Value at the end of all payments or interest periods. |
📌 What Is an Annuity?
An annuity is a financial situation where equal payments are made at regular intervals, such as every month or every year.
In this syllabus, payments are assumed to be made at the end of each period (an ordinary annuity).
- Savings annuity: you regularly deposit money into an account and it grows with interest.
- Repayment annuity: you repay a loan in regular instalments (e.g. mortgage, car loan).
Retirement plans, student loans, credit card repayments and phone contracts all rely on annuity ideas.
📌 Amortization of a Loan
To amortize a loan means to pay it off completely by making regular payments that cover:
- the interest charged for that period
- plus a portion of the original amount borrowed (principal)
At the beginning, a larger share of each payment goes to interest; later payments contain more principal.
Technology (GDC or spreadsheet) is used to work out the fixed payment and, if needed, an amortization table.
Example idea (no hand formula required):
- Borrow 200 000 at 6% per year, repaid monthly over 25 years.
- Technology finds the monthly payment and can show how much of each payment is interest versus principal.
Students can analyse real or simulated loans (credit card, car, housing) and compare the total interest paid under different rates or terms.
📌 Understanding the Time Value of Money
Money now is usually worth more than the same amount later, because it can earn interest.
Annuity calculations balance:
- the present value (loan or initial investment)
- regular payments (PMT)
- interest rate per period
- number of periods
- future value, often 0 for loans (fully repaid) or positive for investments (target amount)
To what extent is the “value” of money a mathematical fact versus a social agreement affected by inflation and risk?
📌 Using GDC / Spreadsheets for Annuities
In this topic you are not required to memorise the annuity formulas.
Instead, you must be comfortable using technology to set up the correct values.
- Select a TVM (Time Value of Money) solver on your GDC, or build a spreadsheet with columns for period, interest and balance.
- Enter known values: n, interest rate per period, PV, PMT or FV, depending on the question.
- Solve for the missing quantity (usually PMT, n or FV).
- Check that the sign convention is consistent: payments (money out) and balances (money in) must have opposite signs.
Always clear the TVM variables before a new question and check that the interest rate you enter is the
rate per period (for example, yearly rate divided by 12 for monthly payments).
📌 Typical Question Types
- Find the regular payment needed to repay a loan in a given time.
- Find how long it will take to clear a loan with fixed payments.
- Find the future value of regular savings into an account.
- Compare two loan options with different interest rates or durations.
Sketch a quick time line (0, 1, 2, …, n) showing when payments occur.
This helps you decide whether you are dealing with a loan being repaid (PV known, FV = 0) or a savings plan (PV = 0, FV unknown).
📌 Ethical & Real-Life Considerations
Annuities and amortization are not just calculations — they affect real people’s lives.
- High interest rates can make repayments unaffordable and lead to long-term debt.
- Understanding mathematics can protect people from unfair or misleading financial offers.
- Short-term loans with very high rates can appear small per month but create huge total payments.
Design a workshop for younger students or your community on understanding interest, loans and responsible borrowing.