Calc FYI

Simple Interest Formula

$$I = P \times r \times t$$

Variables

Symbol Name Unit Description
$I$ Interest currency Total interest earned or paid.
$P$ Principal currency Initial amount borrowed or invested.
$r$ Annual interest rate decimal Annual rate as a decimal (e.g., 4% = 0.04).
$t$ Time years Duration in years.

Simple Interest Formula

Simple interest accrues only on the original principal, not on previously earned interest:

$$I = P \times r \times t$$

Total amount after interest: A = P + I = P(1 + rt)

Simple vs Compound Interest

Feature Simple Compound
Interest base Principal only Principal + accrued interest
Growth curve Linear Exponential
Better for borrowers Short-term loans Long-term investment
Better for investors Rarely Almost always

For short periods and low rates, the difference is negligible. Over decades, compound interest vastly outperforms simple interest.

When Simple Interest Applies

Simple interest is used for: - Treasury bills (short-term government securities) - Car loans in some jurisdictions - Payday loans (though at extremely high effective rates) - Short-term promissory notes - Some bond coupon calculations (between payment dates)

Practical Calculation

Simple interest is straightforward to compute mentally: - $1,000 at 5% for 3 years: I = 1000 × 0.05 × 3 = $150 - Compare compound: A = 1000 × (1.05)³ = $1,157.63 → I = $157.63

The $7.63 difference seems small at 3 years, but over 30 years at 5%: - Simple: $1,500 interest - Compound: $3,322 interest

This is why compound interest is always preferred for long-term savings.

Derivation & History

Simple interest is one of the oldest financial concepts, used in ancient Mesopotamian grain loans and Roman law. It was the default interest model throughout antiquity and the medieval period, partly because compound interest was associated with usury and was prohibited or restricted by religious law in many cultures.

The formal algebraic expression I = Prt appears in European commercial mathematics textbooks from the 14th century onward as trade and banking expanded. Before compound interest became standard in banking practice (18th century), simple interest governed most formal financial contracts.

Worked Examples

Short-term loan

  1. I = 2000 × 0.08 × 0.5
  2. I = 2000 × 0.04 = $80
  3. Total repayable = $2,000 + $80 = $2,080

Result: Interest = $80; Total = $2,080

Treasury bill

  1. Convert days to years: 91/365 = 0.2493 years
  2. I = 10000 × 0.045 × 0.2493
  3. I = $112.19

Result: Interest earned = $112.19

Edge Cases & Limitations

Time in days: Use t = days/365 (or days/360 for some bond markets — the 'bank year' convention).

Rate mismatch: If the rate is monthly (e.g., 1.5%/month), multiply by months not years: I = P × r_monthly × months.

Partial periods: Simple interest prorates exactly (30-day month = 30/365 year), unlike compound interest which has discrete compounding dates.

Real-World Applications

Simple interest governs most consumer short-term loans in many countries. Treasury bills (T-bills) quoted as discount rates use simple interest for their yield calculation. Payday lenders cite simple daily interest rates that result in very high APRs when annualised. Inter-bank overnight lending (e.g., federal funds rate transactions) uses simple interest because the duration is exactly one day. Some mortgage jurisdictions apply simple interest between monthly payment dates.

Try This Formula

Compound Interest Calculator