25400 · Financial Literacy
Banking, Loans & Amortisation
Week 4 covers consumer banking and debt: the credit-card minimum-payment trap, secured vs unsecured consumer loans, fixed- vs adjustable-rate mortgages, and above all loan amortisation. You compute the level instalment PMT = PV·i/[1 − (1 + i)^−n], split each payment into interest (i × opening balance) and principal, build the schedule, and find the outstanding balance at any point by the retrospective or prospective method. Amortisation is a staple structured question and the payment formula is the same annuity tool from Week 2.
What this chapter covers
- 01Amortised instalment: PMT = PV·i / [1 − (1 + i)^−n] (loan principal = PV of the payment annuity)
- 02Splitting a payment: Interest_t = i × Balance_{t−1}; Principal_t = PMT − Interest_t; Balance_t = Balance_{t−1} − Principal_t
- 03The four amortisation principles: level instalment; early payments mostly interest; principal share rises; longer term = more total interest
- 04Prospective outstanding balance = PV of remaining payments = PMT·[1 − (1 + i)^−(n−t)] / i
- 05Retrospective outstanding balance = PV·(1 + i)^t − PMT·[(1 + i)^t − 1] / i (same answer)
- 06Total repayment = PMT × n; Total interest = (PMT × n) − Principal
- 07Credit-card minimum-payment trap; payoff time n = −ln(1 − i·B/PMT) / ln(1 + i)
- 08Secured vs unsecured loans; fixed vs adjustable mortgages; comparing true cost via APR; Excel PV, PMT, NPER
First two rows of a loan amortisation schedule
- +1Instalment: PMT = PV·i / [1 − (1 + i)^−n] = 20,000 × 0.08 / [1 − 1.08^−5] = 1,600 / 0.31942 = $5,009.13.
- +1Payment 1: interest = 0.08 × 20,000 = $1,600; principal = 5,009.13 − 1,600 = $3,409.13; closing balance = 20,000 − 3,409.13 = $16,590.87.
- +1Payment 2: interest = 0.08 × 16,590.87 = $1,327.27; principal = 5,009.13 − 1,327.27 = $3,681.86; closing balance = 16,590.87 − 3,681.86 = $12,909.01. Notice the principal share rose ($3,409 → $3,682) as the interest fell.
- +1Total repayment = 5,009.13 × 5 = $25,045.65, so total interest = 25,045.65 − 20,000 = $5,045.65.
Key terms
- Amortisation
- Repaying a loan with equal instalments that each cover the period's interest plus some principal. Over the term the interest portion falls and the principal portion rises, and the balance reaches zero at the final payment.
- Instalment (PMT)
- The constant periodic payment on an amortising loan, PMT = PV·i/[1 − (1 + i)^−n]. It is identical to the annuity payment formula, because the loan principal equals the present value of the payment stream.
- Interest vs principal split
- For payment t, Interest_t = i × Balance_{t−1} and Principal_t = PMT − Interest_t. Early payments are mostly interest because the balance is large; later payments are mostly principal.
- Prospective method
- Outstanding balance = present value of the remaining payments, Balance_t = PMT·[1 − (1 + i)^−(n−t)]/i. It looks forward at what is still owed.
- Retrospective method
- Outstanding balance = future value of the original principal minus the future value of payments made, Balance_t = PV·(1 + i)^t − PMT·[(1 + i)^t − 1]/i. It looks backward and gives the same balance as the prospective method.
- Minimum-payment trap
- On revolving credit-card debt, paying only the low minimum (often 2-4% of the balance) means most of each payment covers interest, so the balance falls slowly, the term stretches out for years and total interest balloons.
Banking, Loans & Amortisation FAQ
Why does the interest portion of each payment fall over time?
Because interest is charged on the outstanding balance, and that balance shrinks as principal is repaid. With a level instalment, less interest each period leaves more of the fixed payment to knock down principal, so the principal share rises and the balance falls faster later in the term.
Retrospective or prospective — which should I use?
Either; they always give the same outstanding balance. The prospective method (present value of the payments still to come) is usually quicker if you know the instalment and periods remaining; the retrospective method (original principal grown, less payments grown) is handy when you are tracking from the start. Use whichever the data makes easier.
How does the minimum-payment trap actually work?
A card charges interest that compounds on the unpaid balance, and the minimum payment is a small percentage of that balance. Because most of a minimum payment is interest, the principal barely moves; and as the balance falls the minimum falls too, extending the term. Paying a fixed amount above the minimum dramatically cuts both the payoff time and the total interest.
Is amortisation examinable?
Yes — building a short schedule (instalment, then the interest/principal split and balance for the first couple of periods) and finding an outstanding balance are staple structured questions, and the payment formula carries into the group financial model. Rehearse it for the timed quizzes.
Assessment move
Treat the loan instalment as the Week-2 annuity payment formula in disguise — the principal is the present value of the repayment annuity — so PMT = PV·i/[1 − (1 + i)^−n]. Drill the schedule loop until it is mechanical: interest = rate × previous balance, principal = instalment − interest, new balance = previous − principal, repeat. Learn both outstanding-balance methods and check one against the other. Understand the minimum-payment trap qualitatively (why a low percentage payment stretches the term) and be able to use NPER for payoff time. Practise a short schedule and a balance-at-period-t under time pressure for the quizzes, and ask Sia to generate a fresh loan and verify your interest/principal split each row.
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