Simple vs Compound Interest: Formulas and Examples
Simple interest is calculated only on the principal, the amount you borrow or invest. Compound interest is calculated on the principal plus earlier interest left in the balance, so interest earns interest. For example, $6,000 at 4% for three years earns $720 of simple interest but $749.18 compounded annually, a $29.18 difference.
Both methods give the same interest in the first compounding period, the first stretch of time before interest is added to the balance. The gap opens up after that, and it keeps growing the longer the money stays invested.
For accounting students, this distinction explains why identical deposits and stated rates can produce different ending balances. All examples below are hypothetical and assume fixed rates, no fees or taxes, and no additional deposits or repayments unless stated.
Watch: Simple vs. compound interest
Watch Professor Farhat compare simple and compound interest, adjust time for partial years, and calculate accumulated balances. This selected segment runs from 7:45 to 13:07.
Jump to a topic: 7:45 simple interest formula, 8:40 prorating time for months or days, 10:00 compound interest year by year, and 11:41 the future value factor.
What is the difference between simple and compound interest?
| Feature | Simple interest | Compound interest |
|---|---|---|
| Interest base | Principal only. Earlier interest is never added to the base. | Principal plus accumulated interest retained in the balance. |
| Growth over equal periods | The same dollar interest each period at a fixed rate. | Increasing dollar interest at a positive fixed rate. |
| Ending-balance calculation | P + (P × r × t). | P × (1 + i)n. |
Here, P means principal, r is an annual simple rate, t is time in years, i is the rate per compounding period, and n is the number of compounding periods. The n in the compound formula is an exponent, so read it as P × (1 + i) raised to the power of n. Keep your time units consistent, too: i and n must use the same period.
The U.S. Securities and Exchange Commission’s Investor.gov explanation of compound interest describes the effect of earning interest on earlier interest.
How to calculate simple interest
Simple interest = Principal × Annual rate × Time in years
Hypothetical example. Cedar Print borrows $7,200 for eight months at 7.5% annual simple interest. The principal does not change during the term.
Interest = $7,200 × 0.075 × 8/12 = $360. Total repayment = $7,200 + $360 = $7,560.
The 8/12 converts months to years because the rate is annual. Using 8 would charge eight years of interest. Using 7.5 instead of 0.075 would also overstate the result. Neither mistake has anything to do with simple vs compound interest. Both are unit errors.
What if the question gives days instead of months?
Some problems state the term in days. Then time equals the number of days divided by the days in a year, and the question or contract tells you which year length to use.
With a 360-day year, which is common in commercial lending and many textbook problems, 240 days is 240/360. Cedar Print’s interest would be $7,200 × 0.075 × 240/360 = $360.
With a 365-day year, the same 240 days gives $7,200 × 0.075 × 240/365 = $355.07.
Same loan, different day count, different answer. Always check which basis the problem uses before you calculate.
For this basic loan, Cedar Print has $360 of interest expense and its lender has $360 of interest revenue. Repayment of the $7,200 principal is separate from interest. A longer term does not automatically change simple interest into compound interest; the agreement determines the method.
How would Cedar Print record this loan?
Suppose Cedar Print’s fiscal year ends three months after it borrows the money, and it does not use reversing entries (optional entries on the first day of a new year that undo the prior year-end accrual).
When it borrows:
Debit Cash $7,200
Credit Notes Payable $7,200
At year end, it accrues three months of interest ($7,200 × 0.075 × 3/12 = $135):
Debit Interest Expense $135
Credit Interest Payable $135
At maturity, five months later, it repays principal plus all interest:
Debit Notes Payable $7,200
Debit Interest Payable $135
Debit Interest Expense $225
Credit Cash $7,560
Notice the total interest expense across both years is $135 + $225 = $360, which matches the simple interest calculation above.
How do you calculate compound interest?
Accumulated balance = P × (1 + i)n
Total compound interest = Accumulated balance − P
You may also see this written as A = P(1 + r/m)m × t, where A is the ending balance, r is the nominal annual rate, m is the number of compounding periods per year, and t is the number of years. In this lesson, m always means periods per year and n means the total number of compounding periods. The two forms are equivalent because i = r ÷ m and n = m × t.
Hypothetical comparison. Harbor Paper invests $6,000 for three years at 4% per year. Compare simple interest with annual compounding. All interest stays in the account until the end.
| End of year | Simple interest for year | Simple balance | Compound interest for year | Compound balance |
|---|---|---|---|---|
| 1 | $240.00 | $6,240.00 | $240.00 | $6,240.00 |
| 2 | $240.00 | $6,480.00 | $249.60 | $6,489.60 |
| 3 | $240.00 | $6,720.00 | $259.58 | $6,749.18 |
With simple interest, each year produces $6,000 × 4% = $240. Total interest is $720. With compounding, Year 2 earns $6,240 × 4% = $249.60 because the first year’s interest remains invested.
Using the formula, $6,000 × 1.04 raised to the 3rd power = $6,749.184, or $6,749.18. Total compound interest is $749.18. The difference from simple interest is $29.18, after rounding to cents.
Keep full calculator precision through the calculation and round the final answer as required. A table with rounded factors may produce a small difference. For example, a future value table factor of 1.12486 gives $6,000 × 1.12486 = $6,749.16, which is two cents lower. The underlying logic remains the same: the accumulated balance becomes the next period’s interest base.
How would Harbor Paper record compound interest?
Suppose Harbor Paper’s $6,000 sits in a three-year certificate of deposit, interest is added to the deposit each year, and its fiscal year ends on each anniversary of the deposit.
When it invests:
Debit Certificate of Deposit $6,000.00
Credit Cash $6,000.00
End of Year 1:
Debit Certificate of Deposit $240.00
Credit Interest Revenue $240.00
End of Year 2:
Debit Certificate of Deposit $249.60
Credit Interest Revenue $249.60
End of Year 3:
Debit Certificate of Deposit $259.58
Credit Interest Revenue $259.58
At maturity:
Debit Cash $6,749.18
Credit Certificate of Deposit $6,749.18
Notice that interest revenue grows each year because the carrying amount, the balance recorded on the books, grows too. Total interest revenue is $749.18, which matches the compound table above.
Why does compound interest grow faster over time?
With annual compounding, simple and compound interest earn the same amount in the first year. After that, compound growth exceeds simple growth when the rate is positive and earlier interest remains in the balance. If interest compounds more than once a year, compound interest pulls ahead during the first year. For example, $6,000 at 4% compounded quarterly earns $243.62 in year one, compared with $240.00 of simple interest. If interest is withdrawn at each year-end, that withdrawn amount cannot earn more interest in the same account.
Starting earlier creates more periods for growth. For a separate hypothetical example, $1,800 compounded annually at 4% grows to $2,463.42 after eight years but $2,105.75 after four years. The difference comes from time, with the starting amount and rate held constant.
How big does the gap get over 30 years?
Here’s Harbor Paper’s $6,000 at 4% over longer periods, with annual compounding and all interest left in the account.
| Years | Simple balance | Compound balance | Gap |
|---|---|---|---|
| 3 | $6,720.00 | $6,749.18 | $29.18 |
| 10 | $8,400.00 | $8,881.47 | $481.47 |
| 20 | $10,800.00 | $13,146.74 | $2,346.74 |
| 30 | $13,200.00 | $19,460.39 | $6,260.39 |
At 4%, simple interest takes 25 years to double your money. Annual compounding takes about 17.7 years. The Rule of 72, a quick mental shortcut, gets you close: 72 ÷ 4 = 18 years.
What changes when interest compounds quarterly or monthly?
When interest compounds more than once a year, adjust both parts of the formula. Divide the annual rate by the number of periods per year to get i, and multiply the years by that same number to get n.
Take Harbor Paper’s $6,000 at 4% for three years, but compounded quarterly. The rate per quarter is 4% ÷ 4 = 1%, and the number of quarters is 3 × 4 = 12.
$6,000 × 1.01 raised to the 12th power = $6,760.95
Total interest is $760.95. That is $11.77 more than annual compounding, because interest starts earning interest every quarter instead of once a year.
This is also why a 4% rate compounded quarterly works out to an effective annual rate (EAR) of about 4.06%. The EAR is the rate you actually earn over a full year once compounding is counted. You get it by calculating 1.01 raised to the 4th power, minus 1.
Monthly compounding works the same way. The rate per month is 4% ÷ 12, and the number of months is 3 × 12 = 36.
$6,000 × (1 + 0.04 ÷ 12) raised to the 36th power = $6,763.63
Total interest is $763.63. That is $2.68 more than quarterly compounding. Keep the monthly rate at full calculator precision until the end. The effective annual rate here is about 4.07%.
Want to see this worked out? The full lesson covers period conversions at 14:57 and nominal versus effective rates at 16:28.
Which is better, simple or compound interest?
It depends on which side of the money you’re on.
If you’re saving or investing, compounding works for you because your interest earns interest.
If you’re borrowing, compounding works against you when unpaid interest is added to the balance. At the same rate and term, simple interest costs less in that situation, because the lender never charges interest on earlier interest.
One real-world note: “simple interest” on a loan doesn’t always mean the interest stays the same. The Consumer Financial Protection Bureau (CFPB) explains that a simple interest auto loan calculates interest on the outstanding balance, so your principal shrinks as you pay down the loan. Always read the agreement, not just the label.
Common simple vs compound interest mistakes
Reporting the balance as interest. A compound-interest formula usually gives principal plus interest. Subtract principal when the question asks only for earnings.
Compounding only the original amount. Repeating P × i each period is simple interest. For compounding, update the beginning balance or use the exponent formula.
Assuming all short-term agreements use simple interest. A short term can contain several compounding intervals. Read the contract or question rather than inferring the method from the number of years.
Comparing unlike conditions. Hold principal, rate basis, time, withdrawals, and fees constant before attributing a difference solely to compounding.
Mismatching the rate and the periods. Using the annual 4% with 12 quarters gives $6,000 × 1.04 raised to the 12th power = $9,606.19, about $2,845 too high. The right setup is 1% for 12 quarters, which gives $6,760.95.
Why simple vs compound interest matters on the CPA and CMA exams
Compounding is the engine behind the time value of money (TVM), the idea that a dollar today is worth more than a dollar later because it can earn interest.
On the CPA exam’s Financial Accounting and Reporting (FAR) section, TVM shows up in notes receivable and payable, bonds, and leases, where you discount future cash flows using an interest rate. On the CMA exam, the same math drives capital budgeting tools such as net present value. In U.S. GAAP, the FASB guidance on imputing interest on notes, which means assigning a reasonable interest rate when a note’s stated rate is missing or unrealistic, is in ASC 835-30.
Get comfortable with simple vs compound interest now and present value and future value problems become much easier later. For the bigger picture, see the time value of money topics in our Intermediate Accounting course.
Studying for an exam? Try our CPA FAR podcast lessons, practice in the CPA test bank, or start the free CMA Exam Part 2 sample lesson.
Simple Interest and Compound Interest: Interactive Exercise
Practice the simple interest formula, match its symbols to their meanings, and identify how simple interest differs from compound interest.
Complete these seven questions before moving to the worked practice questions. In this exercise, p is principal, i is the rate per period, and n is the number of periods. When you use this formula on your own problems, match the time units and write the rate as a decimal.
Timing reminder: Simple interest can apply over multiple periods. Compounding periods may be shorter than a year; the interest base determines the method.
Review the definitions and formula
What is simple interest? Simple interest is computed on the principal only. It can apply over one or more periods; earlier interest is not added to the interest base.
Interest = p × i × n
- p — Principal
- The amount borrowed or invested.
- i — Interest rate for a single period
- A percentage of the outstanding principal.
- n — Number of periods
- The number of periods, including any fractional period, that the principal is outstanding. Match these periods to the rate: use years for an annual rate and months for a monthly rate.
What is compound interest? Compound interest is computed on the principal plus earlier interest retained in the balance. That retained interest earns additional interest in later compounding periods.
Choose one answer for each question, then select Check answers. You can revise your answers and check again.
Three practice questions with explained answers
1. A five-month simple-interest loan
A hypothetical borrower receives $9,600 at 6% annual simple interest for five months. What interest is owed?
$240. $9,600 × 0.06 × 5/12 = $240. The repayment amount is $9,840, but only $240 is interest.
2. Two years of compound growth
A hypothetical $4,000 deposit earns 5% compounded annually for two years. What are its ending balance and total interest?
Balance: $4,410; interest: $410. $4,000 × 1.05 raised to the 2nd power = $4,410. The second year earns $210, including $10 on the first year’s $200 interest. Simple interest would total $400.
3. Interest withdrawn each year
A hypothetical $2,500 deposit earns 6% annually, but all interest is withdrawn each year. How much remains in the account immediately after the second annual withdrawal?
$2,500. Each year’s $150 interest leaves the account. Two withdrawals total $300, but the remaining principal is still $2,500. Retained interest is necessary for the account’s interest-on-interest effect.
Key takeaways
- Simple interest is calculated on principal only. Compound interest is calculated on principal plus interest left in the balance.
- Both methods give the same interest in the first compounding period. Compounding pulls ahead after that.
- Simple interest: Principal × Rate × Time. Compound balance: P × (1 + i) raised to n.
- The compound formula gives the total balance. Subtract the principal to get interest only.
- Match your units: an annual rate needs time in years, and a quarterly rate needs the number of quarters.
- Read the agreement or question. The length of the term alone does not tell you which method applies.
Frequently asked questions
Is compound interest always larger than simple interest?
For the same positive periodic rate, principal, and more than one period, it is larger when interest remains in the balance. The first compounding period produces the same interest under both methods.
Can simple interest apply for more than one year?
Yes. Duration alone does not determine the method. A stated simple-interest arrangement can cover several years, with interest based on the unchanged principal.
Does the compound-interest formula give interest or total money?
P × (1 + i) raised to n gives the accumulated balance. Subtract P to obtain interest alone.
What is the formula for simple interest?
Interest equals principal × annual rate × time in years. For example, $9,600 at 6% for five months is $9,600 × 0.06 × 5/12 = $240.
How do I handle monthly or quarterly compounding?
Divide the annual rate by the number of compounding periods per year, and multiply the number of years by that same number. For 4% compounded quarterly over three years, use 1% per period for 12 periods.
Is simple or compound interest cheaper for a borrower?
At the same rate and term, simple interest costs less when interest is left unpaid, because the lender never charges interest on earlier interest. If the borrower pays each period’s interest as it comes due, the two methods produce the same total interest.
Which is better, simple or compound interest?
It depends on whether you are saving or borrowing. With the same principal, positive periodic rate, term, and payment timing, compounding earns more for a saver when interest remains invested beyond the first compounding period. For a borrower, simple interest costs less when unpaid interest would otherwise be added to the balance and incur further interest. If each period’s interest is paid when due, the two methods produce the same total interest under otherwise identical terms.
Does compound interest earn more in the first year?
Only if it compounds more than once a year. With annual compounding, year one matches simple interest. On $6,000 at 4%, quarterly compounding earns $243.62 in year one, compared with $240.00 of simple interest.
What is the effective annual rate?
The effective annual rate (EAR) is the rate you actually earn over a full year once compounding is counted. For 4% compounded quarterly, it’s 1.01 raised to the 4th power, minus 1, or about 4.06%.
Keep going with Farhat Lectures
Now that you can tell simple and compound interest apart, the next step is learning how compounding drives present value, bonds, and notes. Work through the full Intermediate Accounting lessons, or brush up on the compounding-period explanation above first if monthly and quarterly rates still feel tricky.
Learn with Farhat Lectures
Strengthen your accounting foundation with clear explanations and guided practice. Explore the free sample course to experience the lessons.
Try the free sample course →
Responses