Simple Interest Calculator

Background.

Lend $10,000 at 5% simple interest and the borrower owes $500 for every year the money is out: $500 after one year, $1,000 after two, $1,500 after three. The debt climbs in a straight line, because the interest is always worked out on the original $10,000 and never on interest that has already built up.

That straight line explains both where simple interest is used and where it misleads. It is the natural rule for money lent for less than a year or repaid in one lump sum: a short note between businesses, a loan to a relative, interest owed for a few months on an overdue invoice, the return on a Treasury bill, the accrued interest a bond buyer hands the seller for the days since the last coupon. Over those spans simple and compound interest come out so close that contracts often use the simpler one.

Any one of the four quantities can be found from the other three. Choose Interest to see what a loan or deposit earns, Principal to find how much must be lent to produce a given sum of interest, Rate to back out the annual rate implied by a known payment, or Time to see how long interest takes to reach a figure. Rates go in as an annual percentage and time in years, with fractions for part-years: 0.5 for six months, 0.25 for a quarter.

Where simple interest misleads is over long periods and on loans repaid in instalments. Across decades, compounding pulls far ahead of the straight line. And many loans whose paperwork says "simple interest", car loans above all, charge interest on a balance that shrinks with every payment, so multiplying the original amount by the rate and the term overstates what they cost. Both cases are worked through in the questions below.

What is simple interest calculator?

Simple interest is interest calculated only on the principal, the sum originally lent or deposited, at a stated rate for a stated time: I = P × r × t. The rate and the time must use the same unit, so an annual rate pairs with a time in years and a monthly rate with a time in months. The amount repaid at the end is the principal plus the interest, A = P + I, which can also be written A = P(1 + rt). Because the base never changes, the interest earned in each year is identical and the balance grows by the same amount every year. Compound interest instead adds each period's interest to the base, so the next period's interest is larger and growth accelerates.

A simple annual rate is also how many loan rates are quoted. A US loan's APR, for example, is the periodic rate multiplied by the number of periods in a year, with no allowance for compounding: 1.5% a month is quoted as an 18% APR, yet if unpaid interest is added to the balance each month, a year of it compounds to about 19.56%. Reading a rate correctly means knowing whether it is simple or compounded.

How to use this calculator.

1. 01Choose what to Solve For: Interest, Principal, Annual Rate or Time.
2. 02Fill in the other three. The Interest field is only read when you are solving for principal, rate or time; when solving for interest, whatever sits in it is ignored, and the same goes for the field you are solving for.
3. 03Type the rate as an annual percentage, so 5 for 5%. If a lender quotes a monthly rate, multiply it by 12 to get the simple annual rate.
4. 04Give the term in years: months ÷ 12, or days ÷ 365. If the contract counts a year as 360 days, which many money-market and commercial loans do, divide the days by 360 instead.
5. 05Read the interest and the total repaid, along with the principal, rate and term, either echoed back or solved.

The formula.

The forward formula is I = P × r × t, with r the annual rate as a decimal (5% is 0.05) and t in years. Each of the other quantities follows by rearranging: P = I ÷ (r × t) when the principal is unknown, r = I ÷ (P × t) when the rate is unknown, and t = I ÷ (P × r) when the time is unknown. In every mode the total is A = P + I.

The interest is directly proportional to each of the three inputs. Double the principal, the rate or the time and the interest doubles; halve any of them and it halves. That proportionality is what makes the rearrangements exact, and it also gives a quick doubling rule: money doubles under simple interest when r × t = 1, so at 5% it takes 20 years, against about 14.21 years with annual compounding.

Two rearrangements cannot be done at a 0% rate. Finding the principal or the time means dividing by the rate, and with no rate there is no principal or time that would produce the interest you entered, so the calculator stops and asks for a rate above zero. Solving for interest or rate at 0% is fine.

A rate found with Solve For Rate is a simple rate. For a lump sum held several years, the equivalent compound annual rate is lower: $1,500 earned on $10,000 over three years is 5% simple, but only about 4.77% a year compounded, since 1.15 raised to the power 1/3 is about 1.0477. Compare like with like before setting such a note beside a savings account's APY.

Day counts matter for short terms. Interest for 90 days at 8% on $5,000 is $98.63 if the year is taken as 365 days and $100.00 if it is taken as 360. The 360-day convention, common in US money markets and many commercial loans, raises the true cost of a quoted rate by a factor of 365/360: a 6% loan charged that way costs about 6.0833% over a full calendar year.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Bodie, Zvi; Kane, Alex; Marcus, Alan J. — Investments, 12th ed., McGraw-Hill, Chapter 5: Risk, Return, and the Historical Record (introduction of simple vs. compound interest).
2. [2]Brealey, Richard A.; Myers, Stewart C.; Allen, Franklin — Principles of Corporate Finance, 13th ed., McGraw-Hill, Chapter 2: How to Calculate Present Values (simple vs. compound interest, time-value of money foundations).
3. [3]Consumer Financial Protection Bureau — Consumer loan education materials covering simple-interest auto loans, personal loans, and prorated interest disclosures under the Truth in Lending Act.
4. [4]U.S. Department of the Treasury, Bureau of the Fiscal Service — Treasury Bill Auction Results and Discount Yield Methodology (the bank-discount and bond-equivalent yield conventions used for T-bills).
5. [5]Federal Reserve Board, Statistical Release H.15 — Selected Interest Rates (canonical source of short-term U.S. money-market rates against which simple-interest estimates can be sanity-checked).