Compound interest is calculated using a straightforward formula: multiply your principal by (1 + r/n) raised to the power of n×t, where r is the annual interest rate, n is how many times per year interest compounds, and t is the number of years. That formula, once you understand its pieces, lets you figure out exactly how much any savings account, loan, or investment will be worth at any point in the future.
The Compound Interest Formula
The standard formula looks like this:
A = P × (1 + r/n)^(n×t)
- A = the final amount (principal plus interest)
- P = the starting principal (the amount you deposit or borrow)
- r = the annual interest rate, written as a decimal (so 5% becomes 0.05)
- n = how many times interest compounds per year (12 for monthly, 365 for daily)
- t = the number of years
Say you deposit $5,000 into a savings account earning 4% interest, compounded monthly. After three years, the math looks like this: $5,000 × (1 + 0.04/12)^(12×3) = $5,636.36. You earned $636.36 in interest without adding another dollar. The key difference between compound and simple interest is that compound interest earns interest on your previously earned interest, not just on your original deposit. Simple interest on that same $5,000 at 4% for three years would only produce $600.
Why Compounding Frequency Matters
The “n” in the formula, how often interest compounds, changes your final balance. More frequent compounding means interest gets added to your balance sooner, and that new, slightly larger balance starts earning interest right away.
Here’s a real comparison. Start with $10,000 in a high-yield savings account at 4%, add $100 a month, and wait five years. With monthly compounding, you end up with $18,861.96. With daily compounding, the same deposits grow to $18,867.01. The difference is only about $5 on a $16,000 total contribution, which shows that compounding frequency matters less than the interest rate itself and how long you leave the money alone.
That said, the gap widens at higher interest rates and over longer time horizons. On a 30-year investment earning 8%, switching from annual to daily compounding can add thousands of dollars. For savings accounts and CDs, daily compounding is the most common. For many loans, interest compounds monthly.
Interest Rate vs. APY
Banks advertise two different numbers, and understanding both will save you confusion. The interest rate (sometimes called the nominal rate) is the base rate your deposits earn. APY, or annual percentage yield, is the effective rate after accounting for compounding. APY is always equal to or slightly higher than the nominal rate.
For example, a savings account with a 4% nominal interest rate that compounds monthly actually grows your money at roughly 4.07% per year once you factor in the compounding effect. That 4.07% is the APY. When you’re comparing savings accounts or CDs, APY is the number to use because it reflects what you’ll actually earn. When you plug numbers into the compound interest formula, though, use the nominal rate and set “n” to match the compounding frequency.
A Worked Example Step by Step
Let’s walk through the formula with a slightly more complex scenario. You invest $8,000 at 6% annual interest, compounded quarterly, for 10 years.
First, convert the rate to a decimal: 6% = 0.06. Next, identify n: quarterly compounding means n = 4. Now plug everything in:
A = $8,000 × (1 + 0.06/4)^(4×10)
A = $8,000 × (1 + 0.015)^40
A = $8,000 × (1.015)^40
A = $8,000 × 1.81402 = $14,512.16
Your $8,000 grew by $6,512.16. To isolate just the compound interest earned, subtract the original principal from the final amount: $14,512.16 minus $8,000 = $6,512.16.
The Rule of 72 Shortcut
If you don’t need an exact number and just want a quick sense of how fast your money will grow, the Rule of 72 is remarkably useful. Divide 72 by your annual interest rate, and you get the approximate number of years it takes for your money to double.
At 6% interest: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years. At 3%: 72 ÷ 3 = 24 years.
You can also flip it around. If you want your money to double in 10 years, you need a return of roughly 72 ÷ 10 = 7.2% per year. The Rule of 72 is an estimate, not precise math, but it’s accurate enough for quick planning and it makes the power of compounding immediately tangible.
How to Calculate It in a Spreadsheet
Both Excel and Google Sheets have a built-in FV (future value) function that handles compound interest without requiring you to type out the formula manually. The syntax is:
FV(rate, nper, pmt, pv, type)
- rate = interest rate per period (annual rate divided by compounding periods per year)
- nper = total number of compounding periods (years × periods per year)
- pmt = any recurring payment per period (use 0 if you’re just calculating growth on a lump sum)
- pv = present value, your starting deposit (enter it as a negative number, since it’s money leaving your pocket)
- type = 0 if payments happen at the end of each period, 1 if at the beginning (0 is the default)
To replicate the earlier example of $8,000 at 6% compounded quarterly for 10 years with no additional contributions, you’d type: =FV(0.06/4, 4*10, 0, -8000, 0). The result is $14,512.16, matching the manual calculation.
If you also contribute $200 per quarter, add that as the pmt argument (again, as a negative number): =FV(0.06/4, 4*10, -200, -8000, 0). The function handles all the compounding math for you, including the compounding on each periodic contribution. One common mistake is mismatching units. If you compound monthly, divide the annual rate by 12 and multiply years by 12. If you compound daily, divide by 365 and multiply by 365.
Compound Interest on Loans
The same formula works in reverse when you’re borrowing money, and it’s just as important to understand on that side. Credit cards, student loans, and mortgages all use compound interest, which means unpaid interest gets added to your balance and you start owing interest on the interest.
On a credit card with a 22% APR compounded daily, a $5,000 balance left untouched for a year grows to about $5,000 × (1 + 0.22/365)^365 = $5,1,245.80 (roughly $1,246 in interest). Making only minimum payments stretches this out even further because each month’s interest is calculated on a balance that includes last month’s interest. This is why paying down high-interest debt aggressively saves far more than the interest rate alone suggests.
What Moves the Needle Most
Three variables control how much compound interest you earn or owe: the interest rate, the time horizon, and how much you start with (or add along the way). Of these, time is the most powerful. Doubling your time horizon doesn’t just double your interest; it can triple or quadruple it because each year’s growth compounds on a larger and larger base.
Starting with $10,000 at 7% compounded annually, after 10 years you have about $19,672. After 20 years, $38,697. After 30 years, $76,123. The interest earned in the last decade alone ($37,426) is nearly four times what you earned in the first decade ($9,672). That accelerating curve is the reason starting early, even with small amounts, makes such a dramatic difference over a lifetime.