Start with the amount and the clock
- Calculate simple and compound interest.
- Understand why the compounding period matters.
- Distinguish savings growth from interest on a loan being repaid.
The principal is the starting amount saved or borrowed. A rate tells you how interest relates to a balance over a specified period. A rate of 5% per year means five per hundred annually under the stated calculation rules. It does not mean 5% every month. Always read the period next to the percentage.
Someone saving money may receive interest; someone borrowing usually pays it. Neither the amount earned nor the amount owed can be understood from the percentage alone. Ask which balance is used, how often interest is calculated, when it is credited or charged, and whether money is being added or removed.
Simple interest: the original principal
With simple interest, the calculation uses the original principal throughout. Save Rs 10,000 at a hypothetical 5% annually, and one year’s interest is Rs 10,000 × 0.05 = Rs 500. Five years earns Rs 2,500, giving Rs 12,500 altogether. The example assumes the principal is unchanged and all interest remains available to you.
The formula is principal × annual rate × years for the interest alone. Add the principal to obtain the ending amount. This is a teaching model, not a promise that a particular savings account or loan uses this method. In particular, a loan advertised with a flat rate needs careful comparison with a reducing-balance loan.
Compound interest: interest can earn interest
With annual compounding, credited interest becomes part of the balance for the next year. The first year still earns Rs 500. The second starts with Rs 10,500, so 5% earns Rs 525. Leaving the interest in place allows the amount earning interest to grow, even without another deposit.
The compound ending amount is principal × (1 + annual rate) raised to the number of years when compounding is annual. Our model keeps full precision and rounds the displayed result to two decimal places. A bank may round each credit and use a specific day-count convention, so its statement can differ slightly.
Try changing one thing at a time
Compare simple interest with annual compounding. These are hypothetical constant rates, with no further deposits, withdrawals, fees, taxes or inflation. Change one input, then explain why the ending balance changes.
Comparison results
| Years | Simple interest | Annual compounding |
|---|---|---|
| 0 | Rs 10,000.00 | Rs 10,000.00 |
| 1 | Rs 10,500.00 | Rs 10,500.00 |
| 2 | Rs 11,000.00 | Rs 11,025.00 |
| 3 | Rs 11,500.00 | Rs 11,576.25 |
| 4 | Rs 12,000.00 | Rs 12,155.06 |
| 5 | Rs 12,500.00 | Rs 12,762.82 |
Simple interestAnnual compounding
Frequency changes the comparison
A nominal annual rate compounded monthly is not the same calculation as annual compounding at that numerical rate. Under a simplified monthly model, an annual nominal rate of 12% becomes 1% each month. Reinvesting for twelve months gives an effective annual growth rate of about 12.68%, not 12%. Product terminology and legal disclosure rules vary, so check the stated definition.
Compare products over the same period and using the same assumptions. A promotional rate lasting three months should not be projected unchanged for five years. Minimum-balance conditions, access restrictions and fees can also change what you actually receive.
A loan balance usually moves the other way
For a reducing-balance loan, interest is calculated on the unpaid principal under the contract’s rules. A repayment covers interest and usually some principal. As principal falls, the next period’s interest can fall too, if the rate stays unchanged. This is different from a savings example where nothing is withdrawn and the balance keeps growing.
Unpaid interest may be added to some debts, depending on the agreement. Do not assume every loan compounds like the savings chart, or that every payment reduces the principal. Fees, overdue amounts and the allocation order can matter. Read a repayment schedule to see what a payment actually covers.
Interest is only part of the outcome
An account balance may rise while its purchasing power falls. If prices rise faster than your net savings return, the money buys less despite the higher number on the statement. Fees and any applicable taxes reduce what you keep. This lesson’s examples exclude them so you can see the interest mechanism clearly.
Remember the three checks: the balance being used, the period attached to the rate and what happens to interest after it is earned or charged. Those checks are more useful than memorising a formula without its assumptions.
Key terms
- Principal: the starting amount saved or borrowed.
- Rate: interest expressed relative to a balance and a period.
- Compounding: adding interest to the balance that earns future interest.
- Purchasing power: what your money can buy.
Continue learning and check the sources
Plan a savings goal (the planner excludes interest)
Source: Investor.gov — compound interest
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Next lesson: How do loans work?
Prepared 5 November 2026. Illustrative education, not a bank offer or personalised advice.