Compound interest is the extra money earned when interest is added to the balance and later interest is paid on that larger balance.
Compound interest sounds fancy, yet it’s just a repeatable pattern: earn interest, add it to the balance, earn interest again. Once you see the pattern, you can calculate it on paper, in a spreadsheet, or with a calculator and know exactly what the numbers mean.
You’ll learn the standard formula, a period-by-period method, and a spreadsheet setup for deposits over time.
What Compound Interest Means In Plain Terms
Simple interest pays interest only on the starting amount. Compound interest pays interest on the starting amount plus any interest already added.
Interest gets posted to the balance, then the next period is calculated on the new total.
If you want a definition you can cite, Investor.gov’s “Compound Interest” glossary entry describes it as interest paid on principal and on accumulated interest.
How To Find Compound Interest With The Standard Formula
Most compound-interest questions boil down to three numbers you control and two you read from the account terms.
- P: starting balance (principal)
- r: annual interest rate written as a decimal (6% becomes 0.06)
- t: time in years
- n: compounding periods per year (12 for monthly, 365 for daily, 4 for quarterly)
- A: ending balance after interest is posted
The core equation is:
A = P(1 + r/n)nt
That equation returns the ending balance A. The compound interest earned is the part above the starting amount:
Compound interest earned = A − P
Step 1: Convert The Rate Correctly
Rates are often shown as a percent. Turn it into a decimal by moving the decimal point two places left. 6% becomes 0.06. 0.5% becomes 0.005.
Watch for a rate that is already a decimal. If an account lists 0.045 as the rate, it already means 4.5%.
Step 2: Match The Time Unit To The Compounding
Time t is in years. Monthly compounding uses n = 12 and a time of 2.5 years is still 2.5. Daily compounding uses n = 365 in many textbook problems, while some banks use 360 for certain products. Use the number stated in the terms.
Step 3: Calculate The Ending Balance
Work inside the parentheses first. Then raise it to the power nt. Then multiply by P.
Mini Walkthrough
Say you deposit $1,000 at 6% per year, compounded monthly, for 3 years.
- P = 1000
- r = 0.06
- n = 12
- t = 3
A = 1000(1 + 0.06/12)12×3 = 1000(1.005)36
After you compute (1.005)36, multiply by 1000 to get A. Then subtract 1000 to get the interest earned.
If you want to sanity-check your result, the SEC’s Investor.gov compound interest calculator gives the same calculation when you enter principal, rate, years, and compounding frequency. Investor.gov’s compound interest calculator also lets you add a monthly contribution.
Common Variations That Change The Inputs
Real accounts come with little twists: deposits over time, withdrawals, fees, rates that change, or a quoted APY instead of a plain rate. Once you spot which twist you have, you can pick the right method.
When Money Is Added Each Month
Monthly deposits mean each deposit earns interest for a different stretch of time. A spreadsheet keeps the timing straight.
Loans Use The Same Math With A Different Story
Loans and credit cards can add interest to the balance. If you want a plain walkthrough, FDIC Chapter 5 on compound interest explains compounding in everyday terms.
Step-By-Step Method When You Want To See Every Period
If formulas feel abstract, build the balance one period at a time. This is also the safest method when rules are unusual.
- Pick the period (month, day, quarter) that matches the compounding.
- Find the rate per period: period rate = r/n.
- Multiply the current balance by the period rate to get interest for that period.
- Add that interest to the balance.
- Repeat for the number of periods: nt.
This method also shows why daily compounding ends a hair higher than monthly compounding at the same stated rate.
Table 1: Fast Decisions For Real-World Compound Interest Problems
| Situation You Have | What To Use | Watch For |
|---|---|---|
| One deposit, rate and compounding given | A = P(1 + r/n)nt | Convert percent to decimal |
| APY given, no extra deposits | A = P(1 + APY)t | t must be in years |
| Monthly deposits added | Spreadsheet or annuity equation | Deposit timing (start or end of month) |
| Daily compounding mentioned | n = number of days per year | Use 365 or 360 based on terms |
| Rate changes over time | Split into segments | Restart A as new P each segment |
| Loan balance grows during no-payment period | Period-by-period buildup | When interest is capitalized |
| You need the interest only | Compute A, then subtract P | Don’t subtract after each period |
| You need the balance at many dates | Spreadsheet table of periods | Round only at the end |
How To Find Compound Interest In A Spreadsheet
A spreadsheet mirrors a statement and it’s easy to audit. You can also plug in deposits, withdrawals, and rate shifts without hunting for a new formula each time.
Set Up Columns That Match The Story
Use one row per period with columns for starting balance, deposit or withdrawal, interest, and ending balance.
Use A Per-Period Rate
If the annual rate is 6% and compounding is monthly, the per-period rate is 0.06/12 = 0.005. Interest for the period equals starting balance × 0.005.
Add Deposits In The Right Place
Some accounts add deposits at the start of a period, others at the end. Pick one and stay consistent. If you’re modeling a paycheck contribution that lands on the first of the month, add it before calculating that month’s interest. If you’re modeling an end-of-month transfer, add it after.
Small Mistakes That Throw Off The Answer
Compound interest problems look similar on the page, so it’s easy to plug in the wrong version of a number. These checks catch most slips.
- Rate mismatch: A monthly rate is not the same as an annual rate. If you already have a monthly rate, don’t divide by 12 again.
- Time mismatch: If the term is 18 months, that’s 1.5 years in the standard equation.
- Rounding too early: Round the final answer, not each period’s interest, unless the question says to round each posting.
- Compounding vs payment schedule: A loan can compound daily while you pay monthly, so pick a period that matches your goal.
Table 2: Reverse Calculations When You Know The Goal
| What You Want To Find | Rearranged Form | Notes |
|---|---|---|
| Interest earned | I = P(1 + r/n)nt − P | I is interest only, not the total balance |
| Starting amount needed | P = A / (1 + r/n)nt | Useful for savings targets |
| Time needed (years) | t = ln(A/P) / (n·ln(1 + r/n)) | Needs natural log on a calculator |
| Rate needed | r = n[(A/P)1/(nt) − 1] | Works when r is fixed through the term |
| Compounding periods per year | Compare results across n values | n is usually set by the account terms |
| Effective annual rate from r and n | EAR = (1 + r/n)n − 1 | EAR is close to APY in many contexts |
| Balance after k periods | Ak = P(1 + r/n)k | Use k as period count, not years |
Rule-Of-Thumb Checks That Keep You Grounded
Once you can compute compound interest, you can also eyeball whether an answer smells right.
Use The Rule Of 72 For A Fast Double-Time Estimate
Divide 72 by the annual rate as a percent. The result is the rough number of years it takes to double. At 6%, 72/6 = 12 years.
The St. Louis Fed’s Open Vault piece on compounding and the Rule of 72 gives a tidy explanation and a sample calculation. St. Louis Fed Open Vault on compound interest also works as a check for the intuition behind the math.
Compare Simple And Compound Interest For The Same Term
Simple interest after t years is P·r·t. If your compound-interest result is lower than simple interest at the same rate and term, a number is off. Compounding never reduces the earned interest when the rate is positive and the balance stays invested.
A Practical Worksheet You Can Reuse
When you face a new compound-interest question, run this sequence. It keeps the setup clean and helps you pick the right tool.
- Write the story in one line: deposit or loan balance, rate, compounding frequency, time, and any regular deposits or payments.
- Circle what the question asks for: ending balance A, interest earned I, starting amount P, time t, or rate r.
- List the known values and convert units: percent to decimal, months to years, days per year if needed.
- Choose the method:
- Use the standard formula for a single deposit with a fixed rate.
- Use period-by-period buildup for odd rules, fees, or mixed schedules.
- Use a spreadsheet when money is added or pulled out over time.
- Compute the ending balance, then subtract the starting balance if the question asks for interest only.
- Run a smell check with the Rule of 72 or by comparing to simple interest.
References & Sources
- U.S. Securities and Exchange Commission (Investor.gov).“Compound Interest.”Plain definition of compound interest as interest on principal plus accumulated interest.
- U.S. Securities and Exchange Commission (Investor.gov).“Compound Interest Calculator.”Calculator that models growth with selectable compounding and optional monthly contributions.
- Federal Deposit Insurance Corporation (FDIC).“Chapter 5: Compound Interest.”Consumer education overview of how compounding works for saving and borrowing.
- Federal Reserve Bank of St. Louis.“How Compound Interest Works & How to Estimate It.”Explanation of compounding and the Rule of 72 as a quick doubling-time estimate.