How to Calculate Interest
Learn how to calculate simple interest, compound interest, daily interest, monthly interest, APR, APY, loan interest, and savings interest with clear formulas and examples.
How to Calculate Interest
Interest is the cost of borrowing money or the amount earned for lending, saving, or investing money.
The two most common types are:
- Simple interest: calculated only on the original amount
- Compound interest: calculated on the original amount plus previously earned interest
For simple interest, use:
Interest = Principal × Rate × Time
For compound interest, use:
Final Amount = Principal × (1 + Rate/Compounds per Year)^(Compounds per Year × Time)
The right formula depends on whether interest is simple or compounded.
Key Interest Terms
Before calculating interest, identify these values:
| Term | Meaning |
|---|---|
| Principal | Starting amount borrowed, saved, or invested |
| Rate | Interest rate, usually written as an annual percentage |
| Time | Length of time, usually in years |
| Interest | Amount earned or charged |
| Final amount | Principal plus interest |
For example, if you deposit $1,000 at 5% annual interest:
Principal = $1,000
Rate = 5% = 0.05
Time = 1 year
The rate must be converted from a percentage to a decimal before using most formulas.
5% = 0.05
12% = 0.12
3.5% = 0.035
Simple Interest Formula
Simple interest is calculated only on the principal.
Use:
I = P × r × t
Where:
I= interestP= principalr= annual interest rate as a decimalt= time in years
The final amount is:
A = P + I
or:
A = P × (1 + r × t)
Simple Interest Example
Suppose:
Principal = $2,000
Annual rate = 6%
Time = 3 years
Convert the rate:
6% = 0.06
Use the formula:
I = P × r × t
Substitute:
I = 2,000 × 0.06 × 3
Calculate:
I = 360
So the simple interest is:
$360
The final amount is:
2,000 + 360 = 2,360
Final amount:
$2,360
Compound Interest Formula
Compound interest is calculated on the principal and on interest already earned.
Use:
A = P × (1 + r/n)^(n × t)
Where:
A= final amountP= principalr= annual interest rate as a decimaln= number of compounding periods per yeart= time in years
The interest earned is:
Interest = A - P
Common compounding frequencies:
| Compounding | n |
|---|---|
| Annually | 1 |
| Semiannually | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
Compound Interest Example
Suppose:
Principal = $1,000
Annual rate = 5%
Compounding = monthly
Time = 3 years
Convert the rate:
5% = 0.05
Monthly compounding means:
n = 12
Use:
A = P × (1 + r/n)^(n × t)
Substitute:
A = 1,000 × (1 + 0.05/12)^(12 × 3)
Calculate:
A ≈ 1,161.47
Interest earned:
1,161.47 - 1,000 = 161.47
So after 3 years, the account has approximately:
$1,161.47
The compound interest earned is approximately:
$161.47
Simple Interest vs Compound Interest
Simple interest grows at a steady amount each period.
Compound interest grows faster because interest starts earning interest.
Example with $1,000 at 5% for 5 years:
| Method | Final Amount | Interest |
|---|---|---|
| Simple interest | $1,250.00 | $250.00 |
| Compound annually | $1,276.28 | $276.28 |
| Compound monthly | $1,283.36 | $283.36 |
The more often interest compounds, the more the final amount can grow, assuming the same stated annual rate.
How to Calculate Monthly Interest
For a monthly interest estimate, divide the annual rate by 12.
Use:
Monthly Interest Rate = Annual Rate ÷ 12
Then:
Monthly Interest = Balance × Monthly Interest Rate
Example
Suppose:
Balance = $5,000
Annual rate = 12%
Convert the annual rate:
12% = 0.12
Monthly rate:
0.12 ÷ 12 = 0.01
Monthly interest:
5,000 × 0.01 = 50
Estimated monthly interest:
$50
This simple monthly estimate is useful for understanding the cost of interest, but actual loan and credit card calculations may depend on daily balances, payment timing, fees, and lender rules.
How to Calculate Daily Interest
For a daily interest estimate, divide the annual rate by the number of days in the year.
Use:
Daily Interest Rate = Annual Rate ÷ 365
Then:
Daily Interest = Balance × Daily Interest Rate
Example
Suppose:
Balance = $10,000
Annual rate = 7.3%
Convert:
7.3% = 0.073
Daily rate:
0.073 ÷ 365 = 0.0002
Daily interest:
10,000 × 0.0002 = 2
Estimated daily interest:
$2 per day
Some products use 360 days, 365 days, or actual-day calculations. Check the account or loan terms when precision matters.
How to Calculate Interest on a Loan
For a simple estimate of loan interest over a period:
Interest = Principal × Rate × Time
Example
Suppose:
Loan balance = $8,000
Annual interest rate = 9%
Time = 6 months
Convert 6 months to years:
6 months = 0.5 years
Convert the rate:
9% = 0.09
Calculate:
8,000 × 0.09 × 0.5 = 360
Estimated interest:
$360
For installment loans, the actual interest paid depends on amortization. As the balance goes down, the interest charged each period usually goes down too.
How to Calculate Interest on Savings
Savings accounts often use compound interest.
Use:
A = P × (1 + r/n)^(n × t)
Example
Suppose:
Deposit = $3,000
Annual rate = 4%
Compounded monthly
Time = 2 years
Convert:
4% = 0.04
Use:
A = 3,000 × (1 + 0.04/12)^(12 × 2)
Calculate:
A ≈ 3,249.43
Interest earned:
3,249.43 - 3,000 = 249.43
So the account earns approximately:
$249.43
APR vs APY
APR and APY both describe interest, but they are not the same.
APR usually means annual percentage rate. It is commonly used for borrowing costs.
APY means annual percentage yield. It includes the effect of compounding and is commonly used for deposit accounts.
If interest compounds, APY is usually higher than the stated interest rate.
Use:
APY = (1 + r/n)^n - 1
Where:
r= annual rate as a decimaln= compounding periods per year
Example
For a 5% rate compounded monthly:
APY = (1 + 0.05/12)^12 - 1
APY ≈ 0.05116
So:
APY ≈ 5.116%
How to Calculate Interest Rate
If you know principal, interest, and time, you can solve for the simple interest rate.
Start with:
I = P × r × t
Rearrange:
r = I ÷ (P × t)
Example
Suppose:
Principal = $4,000
Interest = $480
Time = 2 years
Calculate:
r = 480 ÷ (4,000 × 2)
r = 480 ÷ 8,000
r = 0.06
Convert to a percentage:
0.06 × 100 = 6%
Interest rate:
6% per year
How to Calculate Time
If you know principal, interest, and rate, you can solve for time with simple interest.
Start with:
I = P × r × t
Rearrange:
t = I ÷ (P × r)
Example
Suppose:
Principal = $5,000
Interest = $750
Annual rate = 5%
Convert:
5% = 0.05
Calculate:
t = 750 ÷ (5,000 × 0.05)
t = 750 ÷ 250
t = 3
Time:
3 years
Common Interest Examples
5% Interest on $1,000 for 1 Year
Simple interest:
1,000 × 0.05 × 1 = 50
Interest:
$50
Final amount:
$1,050
10% Interest on $2,500 for 6 Months
Six months is half a year:
6 months = 0.5 years
Simple interest:
2,500 × 0.10 × 0.5 = 125
Interest:
$125
8% Interest on $12,000 for 3 Years
Simple interest:
12,000 × 0.08 × 3 = 2,880
Interest:
$2,880
Final amount:
12,000 + 2,880 = 14,880
Final amount:
$14,880
Quick Interest Reference
| Task | Formula |
|---|---|
| Simple interest | I = P × r × t |
| Final amount, simple interest | A = P × (1 + r × t) |
| Compound interest final amount | A = P × (1 + r/n)^(n × t) |
| Compound interest earned | Interest = A - P |
| Monthly rate | Annual rate ÷ 12 |
| Daily rate | Annual rate ÷ 365 |
| Simple interest rate | r = I ÷ (P × t) |
| Simple interest time | t = I ÷ (P × r) |
| APY | (1 + r/n)^n - 1 |
Remember to write the interest rate as a decimal in formulas.
6% = 0.06
12.5% = 0.125
0.75% = 0.0075
Common Mistakes
Forgetting to Convert Percent to Decimal
Do not use 5 in the formula for 5%.
Use:
5% = 0.05
Mixing Months and Years
If the rate is annual, time should usually be in years.
For example:
6 months = 0.5 years
3 months = 0.25 years
18 months = 1.5 years
Using Simple Interest When Interest Compounds
Simple interest and compound interest can produce different results.
If an account compounds monthly or daily, use the compound interest formula.
Ignoring Fees
Interest is not always the full cost of borrowing.
Loans and credit accounts may include fees, points, penalties, or other charges.
Confusing APR and APY
APR and APY are related, but APY includes compounding.
When comparing savings products, APY is often the more useful number.
When comparing loans, read the terms carefully and look for total cost, fees, and payment schedule.
Assuming the Balance Never Changes
Loan balances often decrease as payments are made.
Credit card balances may change daily.
Savings balances can change with deposits and withdrawals.
If the balance changes, a one-time formula may only be an estimate.
Frequently Asked Questions
How do you calculate simple interest?
Use:
Interest = Principal × Rate × Time
For example, $1,000 at 5% for 2 years:
1,000 × 0.05 × 2 = 100
Simple interest:
$100
How do you calculate compound interest?
Use:
A = P × (1 + r/n)^(n × t)
Then subtract the principal:
Interest = A - P
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal.
Compound interest is calculated on the principal plus previously earned interest.
How do I calculate monthly interest?
Divide the annual rate by 12, then multiply by the balance.
For example, 12% annual interest on $5,000:
0.12 ÷ 12 = 0.01
5,000 × 0.01 = 50
Monthly interest:
$50
How do I calculate daily interest?
Divide the annual rate by 365, then multiply by the balance.
For example, 7.3% annual interest on $10,000:
0.073 ÷ 365 = 0.0002
10,000 × 0.0002 = 2
Daily interest:
About $2
What does 5% interest mean?
It usually means 5% per year unless another time period is stated.
On $1,000, simple 5% annual interest for one year is:
1,000 × 0.05 = 50
So the interest is $50.
Is APR the same as interest rate?
Not always.
APR is an annualized borrowing cost and may include certain fees depending on the product and disclosure rules.
The stated interest rate may only describe the rate applied to the balance.
Is APY the same as interest rate?
Not always.
APY includes the effect of compounding.
For deposit accounts, APY can be more useful than the stated rate because it shows the yearly yield after compounding.
Related Tools and Source
For repeated compounding examples, use the Compound Interest Calculator. For a simpler principal-rate-time setup, use the Simple Interest Calculator. For an outside explanation of APR as a way to compare borrowing costs, see the CFPB’s APR guide.
Final Thoughts
The easiest way to calculate interest is to first identify whether it is simple or compound.
For simple interest:
I = P × r × t
For compound interest:
A = P × (1 + r/n)^(n × t)
Then remember three habits:
- convert percentages to decimals
- keep time in the same unit as the rate
- check whether compounding, fees, or changing balances affect the real result
These formulas are useful for estimates, but always read the actual account, loan, or credit agreement when money decisions depend on the exact interest calculation.