Debt: nominal vs effective annual interest rate, and payoff strategies (avalanche vs snowball)
Convert nominal rates into effective annual rates, calculate a loan instalment, and compare the avalanche and snowball methods for paying off several debts.
What you will learn
- The difference between the nominal rate, the effective annual rate and the German effektiver Jahreszins.
- How to calculate the monthly instalment and total interest of a loan.
- How the avalanche and snowball methods order your debts.
- Practical rules for overdrafts, credit cards and buy-now-pay-later offers.
Explanation
Nominal and effective interest
The nominal annual rate (in German often Sollzins) is the interest rate stated per year, before taking into account how often interest is charged. If interest is charged monthly, the bank uses one twelfth of the nominal rate each month, and next month's interest is charged on a balance that already includes this month's interest. This is compounding.
The effective annual rate shows the true yearly cost after compounding:
Effective annual rate = (1 + nominal rate ÷ m)m − 1, where m = number of interest periods per year.
Example: 18% nominal, charged monthly: (1 + 0.18 ÷ 12)12 − 1 = 1.01512 − 1 ≈ 19.56%.
In Germany and the rest of the EU, lenders must show consumers the effektiver Jahreszins (annual percentage rate of charge). It includes compounding and the costs the borrower must pay to get the credit, so it is the right number for comparing offers. Optional extras, such as many payment protection insurances (Restschuldversicherung), may not be included.
The loan instalment
Most consumer loans (Ratenkredite) are annuity loans: you pay the same amount every month. The monthly instalment is:
A = P × i ÷ (1 − (1 + i)−n), with P = loan amount, i = monthly rate (nominal ÷ 12), n = number of months.
Types of debt to treat as urgent
- Overdraft (Dispositionskredit): flexible but usually one of the most expensive forms of credit. If you use it for months, replacing it with a cheaper instalment loan and closing the gap can save money.
- Credit card revolving balance: many German cards are charge cards that are settled in full each month. "Revolving" cards charge high interest on any amount not repaid.
Payoff strategies for several debts
Rule 1 for both methods: always pay the minimum on every debt to avoid fees and negative credit entries (see Lesson 9 on SCHUFA). Then put all extra money on one target debt. When it is paid off, add its payment to the next target.
- Avalanche: target the debt with the highest interest rate first. This minimises total interest paid, mathematically.
- Snowball: target the debt with the smallest balance first. You close accounts faster, which some people find motivating. It usually costs a bit more interest.
If quick wins keep you on track, the snowball can be the better choice; if the highest-rate debt is large, the avalanche usually saves noticeably more.
Worked example
Hypothetical example: three debts with invented rates. Interest is charged monthly at nominal rate ÷ 12; no fees, no new spending, rates stay constant.
| Debt | Balance | Nominal rate | Minimum payment |
|---|---|---|---|
| Credit card | €1,200 | 18% | €40 |
| Overdraft | €800 | 12% | €30 (self-set) |
| Consumer loan | €4,000 | 7% | €150 |
Step 1: Total budget = minimums €40 + €30 + €150 = €220, plus €200 extra = €420 per month.
Step 2: Avalanche order: credit card (18%) → overdraft (12%) → loan (7%). Snowball order: overdraft (€800) → credit card (€1,200) → loan (€4,000).
Step 3: Month-by-month calculation (checked with a spreadsheet):
| Method | First debt cleared | Second cleared | All cleared | Total interest |
|---|---|---|---|---|
| Avalanche | Card, month 6 | Overdraft, month 8 | Month 16 | ≈ €344 |
| Snowball | Overdraft, month 4 | Card, month 8 | Month 16 | ≈ €362 |
Step 4: Interpretation. Avalanche saves about €362 − €344 = €18 here, because the balances are small and the period is short. The snowball gives a first "win" two months earlier. Both finish in month 16 because the total monthly payment is the same. The real driver of speed is the €200 extra, not the order.
Instalment check for a separate loan: €10,000, 6% nominal, 36 months. i = 0.06 ÷ 12 = 0.005. A = €10,000 × 0.005 ÷ (1 − 1.005−36) ≈ €304.22. Total paid ≈ €304.22 × 36 = €10,951.90; total interest ≈ €951.90. Effective annual rate ≈ 1.00512 − 1 ≈ 6.17%.
Common mistake
Practice activity
Hypothetical case: (a) A card charges 15% nominal, compounded monthly. Calculate the effective annual rate. (b) You have three debts: A €2,000 at 9%, B €500 at 14%, C €3,500 at 5%. Write the avalanche and the snowball order. (c) Which debt receives your extra payment first in each method?
Show solution
(a) (1 + 0.15 ÷ 12)12 − 1 = 1.012512 − 1 ≈ 16.08%.
(b) Avalanche (highest rate first): B (14%) → A (9%) → C (5%). Snowball (smallest balance first): B (€500) → A (€2,000) → C (€3,500).
(c) In both methods debt B comes first, because it has both the highest rate and the smallest balance. In such cases the two methods agree.
Limitations: real offers may include fees, variable rates and early repayment charges, so compare the effektiver Jahreszins and the contract terms.
Key takeaways
- Effective annual rate = (1 + nominal ÷ m)m − 1; compare offers with the effektiver Jahreszins.
- Pay all minimums, then roll every extra euro onto one target debt.
- Avalanche minimises interest; snowball gives faster first wins at a small extra cost.
- Stop new borrowing first; the size of the extra payment matters most.
Next step
In the next lesson you will compare German bank accounts for saving and learn how deposit protection works.
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