Simple Interest Calculator

Simple Interest

Simple interest is calculated only on the original principal, not on accumulated interest. It's commonly used for short-term loans and investments.

Where I = Interest, P = Principal, R = Rate (annual), T = Time (years)

Comparing Simple vs Compound Interest

Example

$1000 at 5% annual rate for 3 years:

I = $1000 × 0.05 × 3 = $150

Total = $1000 + $150 = $1150

The Simple Interest Formula

Simple interest is calculated only on the original principal — interest never earns interest of its own. That makes the growth perfectly linear: double the time, double the interest.

Where I is the interest, P the principal, r the annual rate as a decimal, t the time in years, and A the total (principal + interest).

Worked example: Invest $10,000 at 5% annual simple interest for 3 years. Convert the rate: r = 0.05. Interest: I = 10,000 × 0.05 × 3 = $1,500. Total: A = 10,000 + 1,500 = $11,500. Note the interest is $500 every year — exactly the same each year.

Solving for Principal, Rate, or Time

The calculator above can work backwards from a known total. Rearranging A = P(1 + rt) gives:

Worked backwards examples: To have $12,000 in 2 years at 4% simple interest, invest P = 12,000/(1 + 0.04 × 2) = 12,000/1.08 = $11,111.11. If $5,000 grows to $6,000 in 4 years, the rate was r = (6,000/5,000 − 1)/4 = 0.2/4 = 5% per year.

Time Units: Years, Months, and Days

The formula needs time in years. Convert shorter periods before multiplying:

Worked examples: A $5,000 loan at 6% for 9 months: t = 0.75, I = 5,000 × 0.06 × 0.75 = $225, total $5,225. An $8,000 deposit at 5% for 90 days: I = 8,000 × 0.05 × (90/365) ≈ $98.63, total $8,098.63.

Where Simple Interest Is Actually Used

• Auto loans: Most car loans use simple interest on the declining balance.
• US Treasury bills: Short-term government securities quote simple-interest yields.
• Promissory notes: Short-term business and personal notes typically use simple interest.
• Family and private loans: Informal agreements, including those at the IRS Applicable Federal Rate.

Most consumer products — credit cards, mortgages, savings accounts — use compound interest instead, which is why comparing the two matters (see the comparison table above).

Common Mistakes to Avoid

• Using the percent instead of the decimal: 5% must enter the formula as 0.05 — using 5 inflates the answer 100×.
• Forgetting to convert months or days: 9 months is t = 0.75, not t = 9.
• Expecting interest on interest: Under simple interest each year's interest is identical — growth is a straight line, not a curve.
• Mixing simple and compound: For multi-year deposits the two diverge fast; make sure the product you are modeling actually uses simple interest.
• Rounding too early: Keep full precision through the multiplication and round only the final dollar figure.

Simple vs. Compound Interest: Head to Head

The gap between linear and exponential growth widens every year. For $10,000 at 8%:

After one year they match; after 20 years compounding has nearly doubled the simple-interest total. Verify the 10-year compound figure: 10,000 × 1.08¹⁰ ≈ 10,000 × 2.158925 = $21,589.25 ✓

Interest-Only Payments

On an interest-only loan the borrower pays just the period's interest, leaving the principal untouched. The monthly payment is simply:

Worked example: A $200,000 interest-only loan at 6%: monthly payment = 200,000 × 0.06 / 12 = $1,000. Every payment is identical because the principal never shrinks — pure simple interest in action.

Day-Count Conventions: 365 vs. 360

For periods under a year, lenders divide by either 365 (actual/365) or 360 (the commercial "banker's year") — and the choice changes the interest. On $1,000,000 at 5% for 90 days:

• Actual/365: 1,000,000 × 0.05 × 90/365 = $12,328.77
• Banker's 360: 1,000,000 × 0.05 × 90/360 = $12,500.00

The 360-day convention favors the lender by about 1.4% — worth checking on any short-term commercial note.

Simple Interest on a Declining Balance

Auto loans quote simple interest, but the balance shrinks with each payment — so interest is recomputed on the remaining balance every month. This is an amortizing loan: fixed monthly payments where the interest portion shrinks and the principal portion grows.

Worked example: Borrow $20,000 at 7% for 5 years (60 monthly payments). Monthly rate: 0.07/12. Payment = 20,000 × (0.07/12) / (1 − (1 + 0.07/12)⁻⁶⁰) ≈ $396.02. Total paid: $23,761.44, so total interest = $3,761.44 — far less than 20,000 × 0.07 × 5 = $7,000, because the balance declines instead of staying at $20,000.

Promissory Note Worked Example

A business signs a 180-day promissory note for $25,000 at 8% simple interest (actual/365). Interest = 25,000 × 0.08 × 180/365 ≈ $986.30; the repayment amount is $25,986.30. Short-term commercial paper works exactly this way.

Simple Interest vs. Amortized Loans: Know Which You Have

Quick-Check Practice Problems

Test yourself with the calculator above, then check the answers:

1. $3,000 at 4% simple interest for 2.5 years → Interest: 3,000 × 0.04 × 2.5 = $300; total $3,300.
2. What rate turns $2,000 into $2,500 in 5 years? → r = (2,500/2,000 − 1)/5 = 0.25/5 = 5% per year.
3. How long for $4,000 at 6% to earn $720 in interest? → t = 720/(4,000 × 0.06) = 720/240 = 3 years.

When Simple Interest Briefly Wins

There is one corner where simple interest out-earns annual compounding: periods shorter than one compounding period. At 8% for 6 months, simple interest pays 8% × 0.5 = 4.00%, while annual compounding gives 1.08^0.5 − 1 ≈ 3.92%. The effect is tiny and vanishes the moment the horizon reaches a full period — but it is a favorite exam trap.