Compound Interest Formula: Calculate It

This calculator works out the future value of an investment or loan using the standard compound interest formula. You enter the starting principal, the annual interest rate, how many times per year interest is compounded, and the number of years, and it returns the total balance at the end. It also shows the compound interest earned, which is the final amount minus your original principal.

Formula

The compound interest formula is:

A = P × (1 + r/n)^n×t

Where:

• A = future value of the investment/loan, including interest (in dollars or any currency)
• P = principal, the initial amount deposited or borrowed (same currency as A)
• r = annual nominal interest rate as a decimal (e.g., 5% = 0.05). In the calculator above you enter 5, and the formula divides by 100 to convert it.
• n = number of times interest is compounded per year (e.g., 12 for monthly, 1 for yearly, 365 for daily)
• t = time the money is invested or borrowed for, in years

The exponent n×t is the total number of compounding periods. For example, 10 years compounded monthly gives 120 periods.

Worked Example

Using the default values from the calculator: P = $1,000, r = 5% (0.05 as decimal), n = 12 (monthly), t = 10 years.

1. Divide the annual rate by the number of periods per year: 0.05 / 12 = 0.0041666667
2. Add 1: 1 + 0.0041666667 = 1.0041666667
3. Calculate the exponent: n × t = 12 × 10 = 120
4. Raise to the power: 1.0041666667¹²⁰ ≈ 1.647009497
5. Multiply by principal: $1,000 × 1.647009497 ≈ $1,647.01

The calculator gives the same result: A = $1,647.01. The compound interest earned is $1,647.01 – $1,000 = $647.01.

When to Use Compound vs. Simple Interest

Compound interest applies whenever interest is added to the principal, so the next period’s interest is calculated on the new, larger balance. This is standard for most savings accounts, certificates of deposit, bonds that reinvest coupons, and almost all long-term loans (like mortgages and student loans). Simple interest, where interest is only ever calculated on the original principal, appears in some short-term loans, certain bonds that pay out coupons without reinvesting, and late-payment penalties.

For the same nominal rate and time, compound interest always yields more than simple interest, and the difference grows with time and with higher compounding frequency.

How Compounding Frequency Affects the Result

The value of n changes how often interest is credited. More frequent compounding (daily vs. yearly) produces a slightly higher future value because interest starts earning interest sooner. For example, $1,000 at 5% annual for 10 years:

• Yearly (n=1): $1,628.89
• Monthly (n=12): $1,647.01
• Daily (n=365): $1,648.66

The difference between monthly and daily is small for typical rates and terms. The maximum possible effect is called continuous compounding, which uses the formula A = P × e^r×t. For the same example, continuous compounding gives $1,648.72—only 6 cents more than daily.

Common Mistakes and How to Avoid Them

• Using the percentage number directly in the formula. Always convert the rate to a decimal: 5% becomes 0.05. The calculator above does this automatically, but if you use the formula by hand, forgetting this step is the most frequent error.
• Mixing up time units. If your investment term is 18 months, use t = 1.5 years, not 18. The formula expects time in years.
• Rounding intermediate steps too early. Keep at least 4–6 decimal places during calculations. Rounding 1.0041667 to 1.004 before raising to the 120th power can change the result by several dollars.
• Confusing the annual percentage rate (APR) with the annual percentage yield (APY). APR is the nominal rate r. APY is the effective annual rate after compounding, calculated as (1 + r/n)ⁿ – 1. For monthly compounding at 5%, APY ≈ 5.116%.

Limits of the Formula

The formula assumes a constant interest rate for the entire term. In reality, banks can change rates on variable accounts, and some products offer promotional rates that expire. It also assumes no additional deposits or withdrawals. If you plan to add money regularly, you need the future value of a series formula, not this one.

For loans, the formula gives the total amount owed if no payments are made until the end. Real loans require periodic payments, which reduce the balance, so the actual interest paid is lower. This formula is best for lump-sum investments or for understanding how compounding works, not for amortized loan schedules.

Frequently Asked Questions

What is the difference between compound interest and simple interest?

Simple interest is calculated only on the original principal each period. Compound interest is calculated on the principal plus any interest already earned. For example, $1,000 at 5% simple for 3 years earns $50 each year, total $1,150. Compound annually earns $50 the first year, $52.50 the second, and $55.13 the third, total $1,157.63.

How do I calculate compound interest in Excel?

Use the FV function: =FV(rate, nper, pmt, [pv], [type]). For monthly compounding at 5% for 10 years on $1,000, enter =FV(0.05/12, 10*12, 0, -1000). The result is $1,647.01. The payment is 0 because you are not adding money. The present value is negative because it is money going out.

What is the rule of 72?

The rule of 72 is a quick mental shortcut to estimate how long it takes money to double at a given annual rate. Divide 72 by the annual rate (as a percentage). At 6%, it takes about 72/6 = 12 years. This is an approximation that works best for rates between 4% and 10%.

Does compound interest work for debts too?

Yes. If you carry a balance on a credit card and do not pay it off, interest is added to the balance, and the next month’s interest is charged on that higher amount. This is why credit card debt can grow quickly. Most credit cards compound daily, so the effective rate is higher than the stated APR.

What is continuous compounding?

Continuous compounding is the theoretical limit of compounding infinitely often. The formula is A = P × e^r×t, where e ≈ 2.71828. It yields the highest possible future value for a given nominal rate and time, but in practice the difference from daily compounding is negligible for typical rates.

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in p | Principal | $ | 1000 | 0
in r | Annual interest rate | % | 5 | 0
in n | Compounding periods per year | - | 12 | 1
in t | Time | years | 10 | 0
out A | Future value | $ | p * (1 + r/100/n)^(n*t) | 2
out I | Compound interest | $ | A - p | 2