Simple Interest Calculator

What is Simple Interest?

Simple interest is interest figured only on the original amount borrowed or deposited. Interest that has already accrued is never added to the base, so the charge or payment for each period stays the same from start to finish. A $10,000 deposit at 5% simple interest earns $500 in the first year, $500 in the fifth and $500 in the twentieth. The balance grows in a straight line rather than the upward curve you see with compounding, which makes simple interest easy to predict and easy to check by hand.

Simple Interest Formula

Interest equals principal times rate times time. With the end balance B = P + I, the same relationship can be turned around to find any one value from the other three, which is what the Calculate choice above the form does.

Worked example: you lend $20,000 at 3% a year for 10 years. Interest = $20,000 × 0.03 × 10 = $6,000, so the borrower repays $26,000. Each year adds exactly $600.

Going the other way, suppose you want $30,000 in 10 years from a $20,000 deposit. The needed rate is ($30,000 ÷ $20,000 − 1) ÷ 10 = 0.05, or 5% a year. At 3%, the same goal would take ($30,000 ÷ $20,000 − 1) ÷ 0.03 ≈ 16.7 years, and to reach it in 10 years at 3% you would need to start with $30,000 ÷ 1.3 ≈ $23,077.

Things to watch when using the formula:

• Express the rate as a decimal: 3% becomes 0.03.
• Match units. An annual rate goes with years; a monthly rate goes with months. Six months at an annual rate is t = 0.5.
• Short-term loans sometimes count days: t = days ÷ 365 (or ÷ 360 under some banking conventions), which changes the result slightly.
• The formula gives interest only. Add the principal back to get the total repaid or the ending balance.

I = P × r × t, B = P(1 + rt)

I

interest earned or owed

P

principal, the starting amount

r

interest rate per year, as a decimal

t

time in years

B

end balance

Rearranged: P = B ÷ (1 + rt), r = (B ÷ P − 1) ÷ t, and t = (B ÷ P − 1) ÷ r. Keep the rate and the time in the same unit: a monthly rate pairs with a term in months.

What Financial Instruments Use Simple Interest?

Several common products charge or pay interest this way. Many auto loans and personal installment loans accrue simple interest daily on the outstanding principal, so paying early or extra cuts the interest you owe. Most US Treasury notes and bonds and many corporate bonds pay a fixed coupon on face value that is not reinvested for you, which works like simple interest from the holder's point of view. Certificates of deposit that pay interest out rather than adding it to the balance behave the same way, as do short-term commercial and personal loans, and late-payment interest set by contract or statute. Credit cards, savings accounts and most mortgages, by contrast, involve compounding or amortization.

Simple Interest Versus Compound Interest

Compound interest adds each period's interest to the balance, so the next period's interest is calculated on a larger number. Over one period the two methods give the same answer; after that, compound interest pulls ahead, and the gap widens with time and with higher rates. $10,000 at 6% for 20 years earns $12,000 under simple interest but about $22,071 with annual compounding. For a saver compounding is better; for a borrower simple interest is cheaper.

Compound Interest Formula

The future value with compounding is A = P(1 + r/n)^(nt), and interest is A − P. Here n is the number of times interest is added each year. Common compounding schedules are:

• Annually: n = 1
• Quarterly: n = 4
• Monthly: n = 12
• Daily: n = 365
• Continuously: A = Pe^(rt)

Which is Better for You: Simple or Compound Interest?

It depends on which side of the money you are on. When you borrow, simple interest keeps costs lower and makes extra payments go further, since the interest never builds on itself. When you save or invest, compound interest works for you, and the longer the money stays put the bigger the advantage. The table above shows $10,000 at 6%: after 20 years compounding has earned about $10,000 more than simple interest. If you receive simple interest payouts, such as bond coupons, reinvesting them yourself turns them into compound growth.

Frequently asked questions

Sources

• Investor.gov – Compound Interest Calculator
• CFPB – Auto loans
• TreasuryDirect – Treasury Notes