simple interest

Also called: simple interest formula

Interest charged only on the original amount: I = P × r × d ÷ 365, with r the yearly rate and d the number of days. The same amount accrues every day; nothing is charged on earlier interest.

Simple interest prices money by the day, always on the original amount:

$I = P \times r \times \frac{d}{365}$

where P is the principal, r the yearly rate and d the number of days between the two dates. It is how the cost of a late invoice, a short loan or an early-payment discount is usually estimated.

To turn a period rate into a yearly one, simple interest multiplies by the number of periods: 1% a day is 365% a year, 3% a month is 36%. When interest is added to the balance and earns interest too, the effective annual rate is higher: (1 + period rate)^periods − 1, so 3% a month is 42.6% a year.

An early-payment discount is simple interest the other way round: d ÷ (1 − d) × 365 ÷ (days saved). 2% for paying on day 10 instead of day 60 costs 2/98 × 365/50 ≈ 14.9% a year.

Example

A 576,000 UAH invoice paid 30 days late, when money costs 24% a year:

I = 576,000 × 0.24 × 30 ÷ 365 = 11,362 UAH, almost 2% of the invoice.

Common mistakes

Counting months instead of days. 1 March to 30 April is 60 days.
Comparing a simple yearly rate with an effective one. 2% a month is 24% simple but 26.8% effective.
Dividing a discount by 100 instead of 98. The base is the money you actually receive.
Rounding the share of the year early. Multiply first, divide by 365 last.

Learn it in the course

Simple interest, days and annualizing · Interest on the original amount, counting days, the cost of paying late or skipping an early-payment discount, and turning a period rate into a yearly one.
Compounding · Growth factors, why −50% then +50% loses a quarter, (1 + r)ⁿ, simple vs compound interest, CAGR with a fractional power, and monthly ↔ yearly rates and churn.