Accrued Interest Calculator

What is Accrued Interest?

Accrued interest is the amount of interest that has been earned or accumulated on a principal amount over a specific period of time, but has not yet been paid out. It's commonly used in various financial contexts, including investments, loans, and savings accounts.

The Accrued Interest Formula

The formula for calculating accrued interest is:

\[A = P(1 + r)^t\]

Where:

• \(A\) = Final amount
• \(P\) = Principal amount
• \(r\) = Annual interest rate (in decimal form)
• \(t\) = Time in years

Step-by-Step Accrued Interest Calculation

1. Identify the principal amount (P), annual interest rate (r), and time period in years (t).
2. Convert the annual interest rate to decimal form (divide by 100).
3. Plug these values into the accrued interest formula.
4. Calculate the final amount (A).
5. Subtract the principal from the final amount to get the accrued interest.

Example Calculation

Let's calculate the accrued interest for a principal of $1,000, an annual interest rate of 5%, over 3 years:

1. \(P = \$1,000\), \(r = 5\% = 0.05\), \(t = 3\) years
2. \(A = 1000(1 + 0.05)^3 = \$1,157.63\)
3. Accrued interest = \$1,157.63 - \$1,000 = \$157.63

Visual Representation

The green portion represents the principal ($1000), and the blue portion represents the accrued interest ($157.63).