How to Calculate Compound Interest (Formula and Excel)

Compound interest is interest on interest. Each period, the interest earned is added to the balance, and the next period’s interest is calculated on the larger amount. Over time, that snowball effect is what makes long-term saving so powerful, and long-term debt so expensive. This guide explains the formula, shows how compounding frequency and regular deposits change the result, and walks through the same calculations in Excel.

The compound interest formula

A = P × (1 + r ÷ n)^(n × t)
interest = A − P

• A is the final amount.
• P is the principal (starting amount).
• r is the annual interest rate as a decimal (6% = 0.06).
• n is the number of times interest compounds per year (1 yearly, 12 monthly, 365 daily).
• t is the number of years.

Worked example: $5,000 at 6% for 15 years

Compounded monthly:

1. Rate per period: 0.06 ÷ 12 = 0.005.
2. Number of periods: 12 × 15 = 180.
3. Growth factor: 1.005¹⁸⁰ = 2.4541.
4. Final amount: 5,000 × 2.4541 = $12,270.47.
5. Interest earned: $7,270.47, more than the original deposit.

The compound interest calculator runs this for any amount, rate and period, with a growth chart.

How compounding frequency changes the result

The same $5,000 at 6% for 15 years:

Compounding	Final amount
Yearly (n = 1)	$11,982.79
Quarterly (n = 4)	$12,216.10
Monthly (n = 12)	$12,270.47
Daily (n = 365)	$12,297.11
Continuous	$12,298.02

More frequent compounding helps, but with diminishing returns. The jump from yearly to monthly is about $288, but from monthly to daily it is only about $27. Continuous compounding is the mathematical limit, A = P × e^(r × t). Banks rarely use it, but it appears in finance courses and some derivatives pricing.

To compare accounts with different compounding, use the effective annual rate, or APY: (1 + r ÷ n)^n − 1. A 6% rate compounded monthly is an APY of 6.17%.

Compound interest with regular deposits

Most real savings add money along the way. With a deposit at the end of each period, the future value is:

A = P × (1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i

i is the rate per period and N is the total number of periods.

Example: the same $5,000 at 6% compounded monthly, plus $100 a month for 15 years:

• Total you deposit: 5,000 + 100 × 180 = $23,000.
• Final amount: $41,352.34.
• Interest earned: $18,352.34, about 80% of what you put in.

The future value calculator handles deposits at the start or end of each period and any compounding frequency.

How to calculate compound interest in Excel

What you want	Formula	Result
Lump sum, monthly compounding	=FV(6%/12, 15*12, 0, -5000)	12,270.47
Lump sum plus $100 a month	=FV(6%/12, 180, -100, -5000)	41,352.34
Effective annual rate (APY)	=EFFECT(6%, 12)	6.17%
Growth rate between two values	=RRI(15, 5000, 12270.47)	6.17%

Excel’s FV uses the cash-flow sign convention, so money you invest is entered as negative and the result is positive. Google Sheets uses the same functions. You can also write the formula directly, =5000*(1+6%/12)^(12*15), which gives the same answer.

Simple vs. compound interest

Simple interest is earned only on the original principal. Compound interest also earns on past interest. Over 15 years at 6%, $5,000 earns $4,500 with simple interest but $6,982.79 with yearly compounding. The gap widens every year. For short loans and some bonds, simple interest is common. Use the simple interest calculator to compare.

Compound interest year by year

Working it out one year at a time shows exactly why it accelerates. $5,000 at 6% compounded yearly:

Year	Interest that year	Balance at year end
1	$300.00	$5,300.00
2	$318.00	$5,618.00
3	$337.08	$5,955.08
4	$357.30	$6,312.38
5	$378.75	$6,691.13

Each year’s interest is 6% of a bigger balance, so it grows by a few dollars every year. With simple interest, it would stay at $300. Over decades, those extra dollars become most of the balance.

Compound interest works against you on debt

Credit cards compound too, usually daily or monthly. A $5,000 balance at 22%, compounded monthly with no payments, grows to about $6,217.98 in a year. That is $1,218 of interest, more than 22% of the starting balance, because each month’s interest is added to the balance and then charged interest itself. Paying debt off early stops compounding on the remaining balance, which is why high-rate debt deserves priority over almost any saving goal except an emergency fund.

Compounding vs. how often interest is paid

An account can compound daily but pay interest into your balance monthly. What matters for growth is the compounding frequency, which is captured in the APY. When comparing savings accounts, compare APYs, not the stated rate or the payout schedule.

Compound interest and inflation

Compound growth is measured in future dollars. To see how much your purchasing power really grows, use the real rate: (1 + interest rate) ÷ (1 + inflation) − 1. At 6% interest and 3% inflation, the real rate is about 2.91%. The $12,270.47 from the monthly example is worth about $7,876 in today’s money after 15 years of 3% inflation. That is still a gain of more than half on the original $5,000, but far less than the headline number suggests. Savings that earn less than inflation lose value even while the balance grows. That is why the interest rate alone isn’t enough to judge a savings account or investment.

The rule of 72

To estimate how long it takes money to double, divide 72 by the annual rate. At 6%, that is about 12 years. The exact answer is 11.9. It works for debt too: an unpaid balance at 18% doubles in about 4 years.

Common mistakes

• Using the annual rate per period. With monthly compounding, divide the rate by 12 and multiply the years by 12.
• Entering the rate as a whole number in formulas. Use 0.06, or 6% in Excel, not 6.
• Comparing rates with different compounding. Convert them to APY first, so you compare like with like.
• Forgetting fees, taxes and inflation. They reduce real growth, sometimes a lot over long periods.
• Treating projections as guarantees. Savings rates change and investment returns vary. Solve “what if” scenarios with the finance calculator to see a range of outcomes.

Frequently asked questions

What is the formula for compound interest?

A = P × (1 + r ÷ n)^(n × t), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year, and t the number of years. The interest earned is A − P.

How do I calculate compound interest in Excel?

Use =FV(rate/n, n*years, 0, -principal). For $5,000 at 6% compounded monthly for 15 years, =FV(6%/12,180,0,-5000) returns 12,270.47. Add a monthly deposit as the third argument, entered as a negative number.

How much difference does compounding frequency make?

Some, but less than people expect. $5,000 at 6% for 15 years grows to $11,982.79 with yearly compounding and $12,270.47 with monthly, about $288 more. Daily compounding adds only about $27 more than monthly.

What is the difference between simple and compound interest?

Simple interest is earned only on the original amount. Compound interest is also earned on interest already added. Over 15 years at 6%, $5,000 earns $4,500 with simple interest but $6,982.79 with yearly compounding.

What is the rule of 72?

Divide 72 by the annual rate in percent to estimate how many years it takes money to double. At 6%, money doubles in about 72 ÷ 6 = 12 years. The exact answer is 11.9 years.