Accurate Interest Calculator

What is Annual Percentage Yield (APY)?

APY is the standardized yield that financial institutions must disclose in the United States for interest-bearing accounts. The Truth-in-Savings Act defines APY as the required disclosure rate for these accounts. Use APY to compare deposit accounts.

What is the “Days In Year” option?

In finance, this is called the “day count convention.”

You can select 360, 365, or 366 days in a year. The “Days In Year” setting affects interest expense calculations when you use simple interest, when you use daily compounding, or when the time span includes a fractional (or stub) period.

What is a fractional period? A fractional period is the extra days between two dates that are not sufficient to complete a full compounding cycle. For example, if compounding is set to “Monthly” and the dates are March 15 to April 20, there are five remaining days. These days form a fractional period—in this case, a fractional month.

Fractional periods may produce results that differ from what you might expect in compound interest calculations. In some cases, a less frequent compounding schedule may produce a higher interest amount than a more frequent compounding schedule.

What is continuous compounding?

Continuous compounding occurs when interest is calculated and reinvested an infinite number of times per period. It represents the mathematical limit of compounding frequency.

What is the impact of negative interest rates?

When interest compounds at a negative rate, the investor effectively pays a fee for holding funds. As a result, the future value becomes less than the present value. To see how this works, try a sample calculation using a calculator that supports negative interest rates—such as this one.

You can use this interest calculator in any of the following ways:

• APY calculator
• Daily interest expense calculator
• Investment interest calculator
• Loan interest expense calculator
• Negative interest rate calculator
• Savings account interest calculator

Because it handles dates accurately, this calculator can also perform date math. For example, given two dates, it can calculate the number of days between them or determine a future (or past) date based on a specified number of days.

Compound Interest Equation

Variable Definitions

P

Principal amount (initial investment)

r

Nominal annual interest rate (expressed as a decimal)

n

Compounding frequency (for example, 1 = annually, 12 = monthly, 52 = weekly, 365 = daily)

t

Total time that interest is applied (in the same time units as r, usually years)

A

Future value (includes both principal and interest)

I

Interest earned.

Calculation Steps

1. Substitute the given values into the compound-interest formula (see Figure 1):
   A = P(1 + r/n)^{tn}, where P = 10,000, r = 5%, n = 12, t = 1.
2. Calculate the periodic rate and update the expression inside the parentheses:
   r/n = 0.05/12 ≈ 0.0041666666667…, so the base becomes:
   (1 + 0.0041666666667…).
3. Simplify the base:
   (1 + 0.0041666666667…) ≈ 1.0041666666667…, keeping the exponent at 12.
4. Compute the accumulation factor:
   (1.0041666666667…)^{12} ≈ 1.05116189788173…, then multiply by the principal 10,000 × 1.05116189788173… ≈ 10,511.6189788173….
5. Round the result to two decimal places for currency reporting:
   A ≈ $10,511.62

Step-by-step Solution – Fig. 2

1. A = 10,000 × (1 + 0.05/12)¹²
2. ≈ 10,000 × (1 + 0.0041666666667…)¹²
3. ≈ 10,000 × (1.0041666666667…)¹²
4. ≈ 10,000 × 1.05116189788173…
5. ≈ 10,511.62
6. I = 10,511.6189788173… – 10,000 = 511.62…

Final Answer

The final answer (A) is approximately 10,511.62, of which 511.62 is interest (I).

Validate the calculator: One-year, monthly compounded interest.

Simple Interest Equation

Variable Definitions

B

Initial balance (the starting principal)

r

Simple annual interest rate (expressed as a decimal)

n

Frequency with which interest is applied (for example, monthly or yearly)

m

Number of time periods that have elapsed

A

Future value of the investment (the principal plus interest)

Calculation Steps

1. Multiply the principal amount ($10,000) by the annual interest rate (0.05) and by the number of time periods (12).
2. Divide the result from Step 1 by 12 (the number of time periods).
3. Add the result from Step 2 to the initial balance.

Step-by-step Solution – Fig. 4

1. 0.05 × 10,000 × 12 = 6,000
2. 6,000 ÷ 12 = 500
3. 500 + 10,000 = 10,500
4. 10,500 – 10,000 = 500

Final Answer

The final amount (A) is 10,500.00, of which 500.00 is interest (I).

Validate the calculator: One-year simple interest.