Compound Interest Calculator

The formula this calculator uses

A = P(1 + r/n)^(nt)

A

Final amount (principal + interest)

P

Starting principal

r

Annual nominal interest rate as a decimal (8% = 0.08)

n

Number of times interest compounds per year

t

Time in years

How to check the result by hand

1. 1

   Convert the percentage rate to a decimal

   Divide the quoted annual rate by 100. An 8% rate becomes 0.08. Skipping this step is the single most common error and inflates the result enormously, because the formula treats the rate as a factor rather than a percentage.

2. 2

   Determine the compounding frequency

   Find n from the account terms: 1 for annual, 2 semiannual, 4 quarterly, 12 monthly, 365 daily. If the terms do not state it, assume monthly for savings products and daily for most cards, but confirm before relying on the number.

3. 3

   Compute the periodic rate

   Divide the annual decimal rate by the number of periods: r ÷ n. With r = 0.08 compounding monthly, the periodic rate is 0.08 ÷ 12 = 0.0066667, or about 0.667% per month.

4. 4

   Count the total number of periods

   Multiply periods per year by the number of years: n × t. Twenty years of monthly compounding is 12 × 20 = 240 periods. This is where the term in years matters — entering months here while r stays annual produces nonsense.

5. 5

   Apply the growth factor

   Add 1 to the periodic rate and raise it to the total period count: (1 + r/n)^(nt). For annual compounding at 8% over 20 years that is (1.08)^20 = 4.660957.

6. 6

   Multiply by principal, then subtract to isolate interest

   A = P × the growth factor gives the final amount. Subtract the original principal to get interest earned. Any difference between two accounts shows up entirely inside the growth factor.