Simple Interest Calculator

I = P × r × t, and the total amount is P + I

P

The principal — the amount the interest is charged on

r

The annual rate, as a decimal rather than a percentage

t

The number of whole years

I

The interest, which is the same amount every year

Use it when the interest genuinely does not compound, which is more often than the compound pages suggest. A late-payment penalty, a court judgment, a simple loan between two people, a term deposit that pays the interest out to you each year rather than leaving it in — all of those are this formula and not the other one. It is also the right way to see what compounding is worth on a deposit: run the same principal, rate and term through both pages and the gap is the value of leaving the interest in. At 10,000, 5% and ten years that gap is 1,470.09, and it grows with the rate and the term. Where simple interest is the wrong model is any account that keeps the interest and pays you later — a savings account, a bond whose coupons are reinvested, a pension pot — because there the balance really does grow.

1. 10,000 at 5% simple interest for ten years

   1. Interest for one year: 10,000 × 0.05 = 500
   2. Interest over ten years: 500 × 10 = 5,000, which is also 10,000 × 0.05 × 10
   3. Total amount: 10,000 + 5,000 = 15,000
   4. Yearly interest: 500 in year one, 500 in year five and 500 in year ten — the same each time

   This is the page's default, and it uses exactly the same numbers as the compound interest page's default. The two answers are 15,000.00 and 16,470.09, and that 1,470.09 difference is entirely what compounding does to the same 10,000 at the same 5% over the same ten years.

2. 25,000 at 8% simple interest for three years

   1. Interest for one year: 25,000 × 0.08 = 2,000
   2. Interest over three years: 2,000 × 3 = 6,000
   3. Total amount: 25,000 + 6,000 = 31,000
   4. Interest as a share of the principal: 6,000 ÷ 25,000 = 24%, which is 8% times three years

   A short high-rate arrangement, the shape a penalty or a bridging loan takes. The share of the principal turns out to be exactly the annual rate multiplied by the number of years, which is true on every simple interest calculation and is a useful check to carry around.

3. 10,000 at 5% simple interest for fifty years

   1. Interest for one year: 10,000 × 0.05 = 500
   2. Interest over fifty years: 500 × 50 = 25,000
   3. Total amount: 10,000 + 25,000 = 35,000
   4. Yearly interest: still 500 — fifty years of interest has not changed what the principal earns

   The same 10,000 at the same 5% over fifty years, and the line is still perfectly straight. Compare this with the compound interest page, where 10,000 at 5% compounded monthly for fifty years is 121,193.83. Over half a century the difference between the two models is not a rounding matter, it is whether the money multiplies by three and a half or by twelve.

Simple interest is the right model for a narrow set of arrangements and the wrong one for most things people call savings. It assumes the interest is never added to the balance and never earns anything itself, which is true for a penalty, a judgment or a loan between two people, and false for a bank account, a bond with reinvested coupons or any pension. It assumes one rate for the whole term, so a variable-rate arrangement or one with a rate step is not covered. It deals in whole years, so anything measured in months or days needs the rate and the term converted first — three months at 5% is 10,000 × 0.05 × 0.25, and this page has no field for that. It ignores the timing of payments entirely: if you repay part of the principal halfway through, the interest stops being simple interest on the original amount from that moment and this page cannot express it. Tax on the interest is not modelled, and neither is inflation, so a fifty-year figure like 35,000 is not 35,000 in today's money — over that span the real answer may well be a loss. Finally, no currency symbol is attached to the amounts.

What is the simple interest formula?

Interest equals principal times rate times time: I = P × r × t. For 10,000 at 5% over ten years that is 10,000 × 0.05 × 10 = 5,000, and the total amount is the principal plus the interest, 15,000. Because the interest is never added to the balance, the amount it is calculated on stays at 10,000 for all ten years, which is what makes the formula a single multiplication rather than a power.

How is simple interest different from compound interest?

Compound interest is added to the balance, so the next period's interest is charged on a larger amount; simple interest is not, so every period charges the same. On 10,000 at 5% over ten years simple interest pays 5,000 and compound interest compounded monthly pays 6,470.09. The difference is nothing at all in year one and everything over decades, which is why the two models diverge so sharply on long terms.

When is simple interest actually used?

Wherever the interest is paid out rather than retained. Late-payment penalties, court judgments, interest on an overdue invoice, a short loan between two people, and a term deposit that transfers the interest to your current account each year are all simple interest arrangements. An account that leaves the interest in place is not, however it is advertised, because the balance it charges interest on has grown.

Why does the yearly interest never change?

Because it is always calculated on the original principal. The 10,000 in the default earns 500 in year one; it is still 10,000 at the start of year ten, so it earns 500 again. That is the whole of the difference between this model and compounding: the principal is frozen, so the interest line is straight, and the total is exactly the annual interest multiplied by the number of years.

How do I work out simple interest for part of a year?

Put the time in as a fraction of a year. Three months is 0.25, so 10,000 at 5% for three months is 10,000 × 0.05 × 0.25 = 125. A 90-day period is usually 90 ÷ 365 = 0.246575, which gives 123.29 on the same figures — check which day count the arrangement specifies, because banks differ and 365 against 360 is a real difference on large amounts.

Does simple interest ever beat compound interest?

Yes, whenever you are the one paying it or receiving it as a payout. A borrower prefers simple interest because the amount owed grows linearly rather than multiplying, and someone who spends the interest each year is indifferent between the two. But for anyone leaving the money in place, compounding always wins, and the gap is the interest the interest would have earned — 1,470.09 on the default example, and far more over longer terms.

• Quarterly Interest Rates — interest charged on a balance, and how it is calculated — Internal Revenue Service (United States)
• Compound Interest Calculator — the compounding model this page is the control against — U.S. Securities and Exchange Commission (Investor.gov)
• H.15 Selected Interest Rates — the published rates a simple interest rate stands in for — Board of Governors of the Federal Reserve System (United States)