Bank interest is calculated using one of two basic methods: simple interest or compound interest. Most savings accounts use compound interest, most auto and mortgage loans use an amortizing formula based on your declining balance, and credit cards use a daily balance method that can rack up charges quickly. Once you understand which formula applies, you can calculate almost any interest charge or earning yourself.
Simple Interest
Simple interest is the most straightforward calculation. The bank multiplies your principal (the amount deposited or borrowed) by the interest rate and the time period. The formula looks like this:
- Interest = Principal × Rate × Time
If you deposit $5,000 into an account paying 4% simple interest for one year, you earn $5,000 × 0.04 × 1 = $200. For two years, it would be $400. The key characteristic of simple interest is that you only earn interest on the original principal, never on accumulated interest. Simple interest is rare in savings accounts but shows up in some CDs and short-term lending products.
Compound Interest
Compound interest is what most bank savings accounts, money market accounts, and CDs actually use. Unlike simple interest, compound interest calculates interest on both your original deposit and any interest that has already been added to your balance. The formula is:
- A = P × (1 + r/n)^(n×t)
In that formula, A is the final amount, P is your starting principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.
Say you deposit $10,000 at 5% interest compounded monthly. After one year, your balance would be $10,000 × (1 + 0.05/12)^(12×1) = $10,511.62. You earned $511.62, which is $11.62 more than you would have earned with simple interest on the same deposit. That gap widens dramatically over longer time periods and with larger balances.
How Compounding Frequency Changes Your Earnings
The “n” in the compound interest formula represents how often interest is calculated and added to your balance. Common compounding frequencies include daily (365 times per year), monthly (12), quarterly (4), and annually (1). The more frequently interest compounds, the more you earn, because each compounding event adds interest to your balance sooner, and the next calculation uses that slightly higher number.
Using the same $10,000 deposit at 5% for one year, here is how compounding frequency affects your earnings:
- Annually: $10,000 × (1 + 0.05/1)^1 = $10,500.00
- Quarterly: $10,000 × (1 + 0.05/4)^4 = $10,509.45
- Monthly: $10,000 × (1 + 0.05/12)^12 = $10,511.62
- Daily: $10,000 × (1 + 0.05/365)^365 = $10,512.67
The difference between annual and daily compounding on $10,000 is about $12.67 in the first year. That gap grows significantly with larger deposits and longer time horizons. When comparing savings accounts, check whether the bank compounds daily or monthly, because it affects how quickly your balance grows.
APY vs. Interest Rate
Banks advertise savings accounts using APY, or annual percentage yield, rather than just the base interest rate. APY reflects the effect of compounding over one year, so it gives you a more accurate picture of what you will actually earn. The formula is:
- APY = (1 + r/n)^n − 1
Here, r is the annual interest rate and n is the number of compounding periods per year. An account with a 4.9% interest rate compounding daily has an APY of (1 + 0.049/365)^365 − 1 = roughly 5.02%. That 5.02% is what the bank will advertise and what you can use to compare accounts apples to apples, regardless of how often each bank compounds.
If you know the APY and your balance, a quick way to estimate your annual interest is simply: Balance × APY. For a $20,000 balance at 4.5% APY, you would earn approximately $900 over one year. To estimate monthly earnings, divide by 12: about $75 per month.
The Rule of 72
If you want a quick estimate of how long it will take your savings to double, divide 72 by the interest rate. At 4% interest, your money roughly doubles in 72 ÷ 4 = 18 years. At 6%, it takes about 12 years. This shortcut works best for rates between 2% and 12% and gives you a ballpark without any calculator.
How Loan Interest Works
Interest on mortgages, auto loans, and personal loans works differently than savings interest. These loans are typically amortized, meaning each monthly payment covers both interest and principal, but the split between the two changes over time.
At the start of the loan, most of your payment goes toward interest because the outstanding balance is at its highest. As you pay down the principal, the interest portion of each payment shrinks and more money goes toward the balance. To calculate the interest portion of any given monthly payment, multiply your outstanding loan balance by your annual interest rate divided by 12.
- Monthly interest = Outstanding balance × (Annual rate / 12)
For example, if you owe $200,000 on a mortgage at 6.5%, your first month’s interest charge is $200,000 × (0.065 / 12) = $1,083.33. Whatever is left from your total monthly payment after covering that $1,083.33 goes toward reducing the principal. Next month, the balance is slightly lower, so the interest charge drops by a few dollars, and a bit more of your payment chips away at the loan itself.
The formula for the total monthly payment on an amortized loan is:
- Payment = Loan Amount × [i × (1 + i)^n] / [(1 + i)^n − 1]
In this formula, i is the monthly interest rate (annual rate divided by 12) and n is the total number of monthly payments. For a $200,000 mortgage at 6.5% over 30 years, i = 0.005417 and n = 360. The monthly payment comes to about $1,264. Over the life of that loan, you would pay roughly $255,000 in interest on top of the $200,000 you borrowed.
How Credit Card Interest Is Calculated
Credit card interest uses the average daily balance method, which is more granular than a simple monthly calculation. Here is how it works step by step:
First, find your daily periodic rate by dividing your card’s APR by 365. A card with a 22% APR has a daily rate of about 0.0603%. Next, the card issuer looks at your balance at the end of each day during the billing cycle. It adds up all of those daily balances and divides by the number of days in the cycle to get your average daily balance. Finally, the issuer multiplies the average daily balance by the daily rate and then by the number of days in the billing cycle.
- Interest charge = Average daily balance × Daily rate × Days in billing cycle
If your average daily balance is $3,000, your APR is 22%, and the billing cycle is 30 days, the math looks like this: $3,000 × 0.000603 × 30 = $54.25 in interest for that month. What makes credit card interest particularly expensive is that most issuers compound daily, meaning each day’s interest gets folded into the next day’s balance. New purchases may also be added to the daily balance immediately, depending on the card issuer’s method.
You can avoid credit card interest entirely by paying your full statement balance by the due date each month. The interest calculation only kicks in when you carry a balance past the grace period.
Putting It All Together
The type of account determines which formula to use. For savings accounts and CDs, use the compound interest formula or simply multiply your balance by the APY for a yearly estimate. For mortgages and car loans, use the amortization formula to find your monthly payment and multiply the outstanding balance by the monthly rate to see how much of any payment goes to interest. For credit cards, divide the APR by 365 and apply it to your average daily balance.
Most banks and lenders provide online calculators that do the math for you, but understanding the formulas lets you verify what you are being charged, compare offers accurately, and make smarter decisions about where to park your savings or how aggressively to pay down debt.