Simple vs Compound Interest: Formulas & Examples
Simple interest = P × r × t. Compound interest = P(1 + r/n)^(nt). Full guide with formulas, examples, and the dramatic long-term difference.
Simple Interest Calculator — Direct Answer
Simple interest is P × r × t (principal × rate × time). $1,000 at 5% for 3 years = $150 interest, $1,150 total. Compound interest is P(1 + r/n)^(nt) — the same $1,000 at 5% compounded monthly for 3 years = $161.47 interest, $1,161.47 total. Compound grows faster over time.
→ Calculate simple interest with our free tool
How to Calculate Simple Interest
Simple interest only accrues on the original principal. It never compounds.
Simple Interest: I = P × r × t
Total Amount: A = P + I = P(1 + rt)
Where:
- P = principal (initial amount)
- r = annual interest rate (decimal)
- t = time in years
How to identify the variables
Example: $5,000 at 6% for 2 years
- P = 5,000
- r = 0.06
- t = 2
How to apply the formula
Example: $5,000 at 6% for 2 years
- I = 5,000 × 0.06 × 2 = $600
- A = 5,000 + 600 = $5,600
How to adjust for months
Divide the months by 12 to convert to years.
Example: $5,000 at 6% for 8 months
- t = 8 ÷ 12 = 0.667
- I = 5,000 × 0.06 × 0.667 = $200
How to Calculate Compound Interest
Compound interest accrues on principal AND accumulated interest.
A = P(1 + r/n)^(nt)
I = A − P
Where:
- n = compounding periods per year
- Annual: n = 1
- Quarterly: n = 4
- Monthly: n = 12
- Daily: n = 365
How to apply the formula
Example: $5,000 at 6% for 2 years, compounded monthly
- n = 12, t = 2
- A = 5,000 × (1 + 0.06/12)^(12×2)
- A = 5,000 × (1.005)^24
- A = 5,000 × 1.1272 = $5,636
- I = $636
Compare to simple: $600. Compound earns $36 more.
How to apply continuous compounding
A = Pe^(rt)
Example: $5,000 at 6% for 2 years, continuous:
- A = 5,000 × e^(0.06×2) = 5,000 × e^0.12 = $5,637
Simple vs Compound Interest Chart
$10,000 at 5% — year by year
| Year | Simple Interest | Compound (Monthly) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,512 | $12 |
| 5 | $12,500 | $12,834 | $334 |
| 10 | $15,000 | $16,470 | $1,470 |
| 20 | $20,000 | $27,126 | $7,126 |
| 30 | $25,000 | $44,677 | $19,677 |
$10,000 at 7% for 30 years
| Compounding | Final Amount | Interest Earned |
|---|---|---|
| Simple | $31,000 | $21,000 |
| Annual | $76,123 | $66,123 |
| Monthly | $81,165 | $71,165 |
| Daily | $81,646 | $71,646 |
| Continuous | $81,659 | $71,659 |
Compounding frequency impact
| Frequency | n | APY at 6% |
|---|---|---|
| Annual | 1 | 6.000% |
| Semi-annual | 2 | 6.090% |
| Quarterly | 4 | 6.136% |
| Monthly | 12 | 6.168% |
| Daily | 365 | 6.183% |
| Continuous | ∞ | 6.184% |
Common Simple/Compound Interest Mistakes
Mistake 1: Using APR for compounding
APR assumes simple interest. APY includes compounding.
Fix: Use APY for savings, APR for loans. They differ by the compounding effect.
Mistake 2: Forgetting to convert months to years
t must be in years. 6 months = 0.5 years.
Fix: Always divide months by 12 before applying.
Mistake 3: Assuming daily compounding matters
Daily vs monthly differ by only 0.015% per year. Not worth chasing.
Fix: Focus on rate and time. Compounding frequency is a minor factor.
Simple vs Compound Interest Use Cases
Simple interest applies to
- Car loans (some)
- Short-term personal loans
- Interest-only mortgages
- Simple savings accounts (rare)
Compound interest applies to
- Savings accounts
- Certificates of deposit
- Credit cards
- Most mortgages
- Investment accounts
Which do you want?
Borrowing: Simple interest is cheaper. Saving: Compound interest grows faster.
Simple Interest Calculator FAQ
What is the simple interest formula?
I = P × r × t. Interest = Principal × Rate × Time. Simple interest doesn't compound.
What is the compound interest formula?
A = P(1 + r/n)^(nt). Amount = Principal × (1 + Rate/Periods)^(Periods × Time).
What is the difference between simple and compound interest?
Simple interest accrues only on principal. Compound interest accrues on principal + accumulated interest.
How much does $10,000 earn in 10 years at 5%?
- Simple: $15,000 ($5,000 interest)
- Compound monthly: $16,470 ($6,470 interest)
Does compound interest apply to loans?
Yes. Most mortgages, credit cards, and student loans use compound interest. Some auto and personal loans use simple interest.
Next Steps for Interest Analysis
- Simple Interest Calculator — Easy I = Prt
- Compound Interest Calculator — Compounding
- Loan Calculator — Full amortization
- APR Guide — True cost
- Amortization Guide — Payment breakdown
Last updated October 2026. Compounding assumes no withdrawals — real accounts vary.