# Interest Rate Calculator

## What is Interest Rate?

Interest rate represents the proportion of borrowed or deposited amount in the bank that has to be paid back or received over the original amount, respectively. This difference embodies interest and is usually expressed as a yearly percentage. Formally, the rate at which a financial institution lends its money or the amount a bank compensates its depositors for holding money in an account is the interest rate.

A significant concept in interest rate is **compounding interest**. It refers to the interest earned over a specific period being added to the principal amount. Hence, the interest calculation base (the principal) encompasses the earlier period's interest, resulting in a total amount that expands exponentially.

Interest rate can be in different forms, each having its distinct features. Familiarity with these forms can aid in distinguishing between them. The typical ones estimated for bank interest rates on a loan or deposit include:

**Nominal Annual Interest Rate (r)****Periodic Rate (i)****Effective Annual Rate (EAR)****Annual Percentage Rate (APR)**

## How to Use the Interest Rate Calculator?

To use the tool, initially, you need to choose the subject of your interest: a loan or a deposit. After that, you can compute the previously mentioned interest rates by specifying the necessary parameters.

Here are the parameters you need to specify:

**Loan amount (A)**: This refers to the loan amount under consideration, which is also the principal.**Term (t)**: This involves the interval over which you need to repay the loan amount and all associated costs (interest and other additional fees).**Interest capitalization frequency (m)**: This is the number of times interest compounding happens in one year. For instance, when compounding is applied annually, m=1, when quarterly, m=4, monthly, m=12, etc.**Payment frequency (q)**: This entails the regularity with which part of the loan is repaid.**Periodic payment (P)**: This is the sum to be paid in each period defined by the payment frequency.**Current balance and Initial Deposit**are required in the case of a deposit account.

Once you set all the necessary fields, the related interest rates will be calculated immediately.

## An Actual Example to Demonstrate the Calculator

Let's say we have a loan amount or principal (A) of **$10,000**, and we need to repay it over a term (t) of **5 years**. Assuming the interest capitalizes annually (m=1), and we repay part of the loan monthly (q=12), with a periodic payment (P) of **$200**.

Plugging these values into the calculator, we calculate the Nominal Annual Interest Rate (r), Periodic Rate (i), Effective Annual Rate (EAR), and Annual Percentage Rate (APR).

Using the formulas, we can verify if the calculator results are accurate. However, note that the results represent an approximate value due to the complexity of actual financial formulas. Such formulas often involve logarithms and cannot be solved analytically without a calculator.