Watch interest earn interest
Interest amount is measured in dollars; interest rate is a percentage per period. Mixing these quantities makes even a correct-looking equation wrong.
Compounding adds $62.00 above simple interest.
Simple interest charges only the original principal: I = PNi.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
Simple interest is proportional to the original principal, the rate, and elapsed periods. Compound interest is charged on the current balance, including accumulated interest. For positive i and N>1, compound growth exceeds simple growth.
Build the calculation
Write the rate as a decimal in formulas and match its period to N. Exact doubling time is ln(2)/ln(1+i); the Rule of 72 estimates years as 72 divided by the annual percentage rate and is only an approximation. Negative growth and changing rates need the stated model, not a fixed simple-interest shortcut.
Set up. Calculate. Explain.
Rebuild the starting scenario
Principal: 2000 $; Interest rate: 10 % per year; Number of years: 3 years. Calculate the compound future balance.
Setup hint
Simple interest charges only the original principal: I = PNi.
Open the visual solution
- Simple interest charges only the original principal: I = PNi.
- Compound interest adds each period's interest to the balance.
- Compound interest amount = F − P = $662.00. Rule of 72 is approximate; exact doubling time is ln 2 / ln(1+i).
Compounding adds $62.00 above simple interest.
Simple interest charges only the original principal: I = PNi.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
Deposit $9,000 for five years at 8% annual compound interest. Find future balance.
Setup hint
Simple interest charges only the original principal: I = PNi.
Open the visual solution
- Simple interest charges only the original principal: I = PNi.
- Compound interest adds each period's interest to the balance.
- Compound interest amount = F − P = $4,223.95. Rule of 72 is approximate; exact doubling time is ln 2 / ln(1+i).
Compounding adds $623.95 above simple interest.
Simple interest charges only the original principal: I = PNi.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Why does compound interest exceed simple interest for positive i and N>1?
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
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