What is an interest rate?
When you save money in a bank, the bank lends it to other people. When you borrow, you use someone else's money now and pay it back later. Interest is the extra money paid for this. The interest rate is that extra as a percentage per year.
Why should a borrower pay extra? Because the lender gives up something:
- Waiting: the lender cannot spend the money now. Most people prefer money today to the same money next year. Interest is the reward for waiting. This swap of money now for money later is called exchange over time (intertemporal exchange).
- Risk: the borrower might not pay back. Interest also pays the lender for this risk.
- Inflation: prices may rise, so the money buys less later.
Interest calculations
Simple interest
Interest is worked out on the starting amount (the principal, P) only. Each year adds the same amount.
Interest = P × r × n ÷ 100, where r is the rate in % and n is the number of years.
Compound interest
Each year's interest is added to the balance, and next year's interest is worked out on the new, bigger balance. This is interest on interest.
Amount = P × (1 + r/100)ⁿ
Example: ₹1000 at 10% for 2 years. Simple: 1000 + 100 + 100 = 1200. Compound: 1000 → 1100 → 1210. The extra 10 is interest on the first year's interest.
Real interest rate
Real rate ≈ nominal rate − inflation. If a bank pays 6% and prices rise 4%, your buying power only grows about 2%.
What sets interest rates?
- The central bank (for example the Reserve Bank of India, the Bank of England, the US Federal Reserve) sets a base rate or policy rate. Banks' own rates move with it.
- Risk of the borrower: a government is very likely to pay back, so it borrows cheaply. A person with no steady income is riskier, so pays more. This extra is the risk premium.
- Collateral: something valuable the lender can take if the loan is not repaid, such as a house for a home loan or a car for a car loan. Collateral lowers the lender's risk, so the rate is lower. A credit card has no collateral, so its rate is very high.
- Time: longer loans usually have higher rates, as more can go wrong.
- Supply and demand for loans: many savers and few borrowers push rates down; the opposite pushes them up.
Effects of interest rates on consumers and producers
| When rates RISE | When rates FALL |
|---|---|
| Saving pays more, so households save more | Saving pays less, so households save less |
| Loans and credit cards cost more, so people borrow and spend less | Loans are cheaper, so people borrow and spend more (cars, houses) |
| People with variable-rate home loans pay more each month and have less to spend | Monthly loan payments fall, leaving more to spend |
| Firms invest less in new machines and buildings, as projects cost more to fund | Firms invest more |
| Total spending falls, which can slow inflation but also growth and jobs | Total spending rises, which can boost growth but also inflation |
This is why central banks raise rates to fight high inflation and cut rates to help a weak economy.
Key formulas and definitions
- Interest rate = interest per year ÷ amount borrowed × 100%
- Simple interest = P × r × n ÷ 100
- Compound amount = P × (1 + r/100)ⁿ
- Compound interest = amount − P
- Real interest rate ≈ nominal rate − inflation rate
Worked examples
1. You save ₹2000 at 5% simple interest for 1 year. How much interest do you get?
Interest = 2000 × 5 × 1 ÷ 100 = ₹100.
2. Find the simple interest on €1500 at 4% for 3 years, and the total.
Interest = 1500 × 4 × 3 ÷ 100 = €180. Total = 1500 + 180 = €1680.
3. £1000 is saved at 10% compound interest for 3 years. Find the amount.
Year 1: 1000 × 1.1 = 1100. Year 2: 1100 × 1.1 = 1210. Year 3: 1210 × 1.1 = 1331. Amount = £1331.
4. A loan of 5000 has interest of 400 in one year. What is the interest rate?
Rate = 400 ÷ 5000 × 100 = 8%.
5. A bank pays 6% and inflation is 4%. Find the real interest rate. What if inflation were 8%?
Real ≈ 6 − 4 = 2%. With 8% inflation: 6 − 8 = −2%, so savings lose buying power.
6. Explain why a home loan has a lower rate than a credit card.
The home loan has the house as collateral, so if the borrower does not pay, the bank can sell the house. Lower risk means a lower risk premium. The credit card has no collateral.
Common mistakes
- Thinking higher rates make people spend more. Higher rates reward saving and make borrowing dearer, so spending falls.
- Using simple interest when the question says compound. Compound adds interest each year before the next year's sum.
- Forgetting inflation. A 5% rate with 6% inflation is a real loss.
- Thinking collateral raises the rate. It lowers the lender's risk, so it lowers the rate.