Simple Interest

Multiply the initial principal K₀ by the annual rate r as a decimal and the duration t in years: Z=K₀rt. For €800 at 3% over two years, Z=800·0.03·2=€48. Enter the rate as 0.03, not 3. The final balance is K_t=K₀+Z=€848. Check the units: a yearly rate times years is dimensionless, so multiplying by currency returns currency. The interest per year stays constant while the principal and rate remain unchanged. The model assumes fixed principal; withdrawals or changing rates require a new balance calculation.

The formula uses t in years when r is an annual rate. Six months therefore means t=0.5, and three months means t=0.25. For €1,200 at 4% annually over six months, Z=1,200·0.04·0.5=€24. A monthly rate may also be used, but the rate and number of periods must match. Do not combine an annual rate with the bare number 6 for six months. A financial contract may prescribe a different day-count convention, which is outside this basic mathematical model. Convert months to a fraction of a year before using a rate stated per year.

The interest formula first gives only the interest amount Z. The final balance after t years is K_t=K₀+Z=K₀(1+rt). With an €800 principal and €48 interest, the result is €848. Do not confuse Z with the entire new balance. Check that the final amount equals initial principal plus interest. If fees, taxes, or withdrawals matter, include them separately in the balance; the simple formula does not include those factors. For short durations, the difference from compound interest may be small, but the models diverge with every period.

With simple interest, each period’s interest is calculated from the initial principal, so the amount per year stays constant. With compound interest, credited interest is added to the balance and earns interest in later periods. Simple interest grows linearly over time, while compound interest grows exponentially. For €800 at 3% over two years, simple interest gives €848; annual compounding gives 800·1.03²=€848.72. The difference is initially small but can grow over long periods. Choose the model stated in the problem. Solving for r gives a decimal; multiply by 100 at the end to state a percentage.

From Z=K₀rt, divide by K₀t to get r=Z/(K₀t). If €48 interest came from €800 over two years, r=48/(800·2)=0.03=3% per year. Enter duration in years and make sure Z and K₀ use the same currency. The formula assumes K₀>0 and t>0. A negative rate or fees would require clarifying the model. Check the result by substituting r back into Z=K₀rt. Interest and principal are monetary amounts; do not confuse interest with the entire amount due. State which quantity the question requests.