## What is an Interest Rate?

When you deposit your money with the bank, the deposit earns you some extra money at the end of the specific period – something more than what you deposited. That amount of money that the bank pays you for keeping the money with the bank is the “interest” and the percentage at which the bank pays you for your amount is called the “interest rate”.

Similarly, when you borrow money from the bank, or when the bank is lending you money, the bank charges you a certain amount of the loan amount again called the “interest” and the percentage that it charges on the loan amount is called “interest rate”. In simple terms, the interest rate is the rate a bank or other lender charges to borrow its money or the rate a bank pays its savers for keeping money in an account.

This interest rate is generally expressed as an annual percentage.

## Simple and Compound Rates

Let us understand the two main interest rates—simple and compound.

**Simple Interest**

Simple interest is interest calculated on the principal portion of a loan or a deposit, at a defined rate of interest. For example, A deposits $1000 in XYZ bank for one year. At the end of one year, the bank pays A $1000 + an interest amount of $20. You can see that the bank has paid an interest of 2% to A on his deposit.

**Formula to Calculate Simple Interest**

When the principal amount, the rate or percentage of interest, and the time period is known, then, you can calculate the simple amount on the principle by using the formula:

$$\text{SimpleInterest(SI)}=\frac{\text{P}\times \text{R}\times \text{T}}{100}$$

Here, principal (P) is the principal or initial amount, interest rate (R) in percentage, and time period (T) is the number of years.

Therefore, to calculate the total money that will be paid back after the specific period, you can calculate using the formula:

$$\text{Amount(A)}=\text{Principal(P)}+\text{SimpleInterest(SI)}$$

**Compound Interest**

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest over the previous period. In simple terms, compound interest is interest paid on interest and this will make the initial amount grow at a faster rate than the simple interest.

Therefore, when the interest rate is compounded, the returns on the principal amount over the long term are significantly higher than when the interest rate is simple.

**Formula to Calculate Compound Interest**

Compound Interest = Amount – Principal

where the amount is given by the formula:

$$\text{A}=\text{P}{\left(1+\frac{\text{R}}{100}\right)}^{\text{n}}$$

Where the interest is compounded annually.

A = Amount

P = principal amount invested or borrowed

R = interest rate

n = number of years

## Other Types of Interest Rates

There are other types of interest rates that we should know when it comes to various loans such as home loans and mortgages.

In loans with a fixed interest rate, as the name suggests, the interest rate remains the same throughout the entire borrowing period. This allows the borrower to have a standard monthly repayment plan. Mortgages and car loans have fixed interest rates.

Loans such as student loans and adjustable-rate mortgages come with variable interest rates. Here, the interest rate changes over time as per market conditions. One point to note is that variable rate loans come with lower interest rates.

Note: The interest rates of Adjustable-rate mortgage (ARM) / variable-rate mortgage change periodically during the life of the loan in accordance with changes in an index such as the U.S. Treasury-Index (T-Bill) or the Secured Overnight Financing Rate (SOFR).

In the case of Annual Percentage Rate (APR), the interest rate is normally charged (or) applied on the amount loaned on an annual basis.

Note: When you apply for a mortgage or a loan, your credit score also has a role in the lenders deciding the mortgage interest rate.

**Further classification of interest rate**

There are essentially three main types of interest rates when we talk about fixed-income investments—nominal interest rate, effective rate, and real interest rate. Let us look at the features of these types of interest rates.

The nominal interest rate or coupon rate is the interest rate that is taken into account before considering inflation. Nominal interest rates are stated actually on bonds and loans and are calculated on simple interest. The central banks try and keep the short-term nominal interest rates or the federal funds rate at a low level so that economic activity is triggered and gives a boost to the economy. However, since inflation is not considered while determining the nominal interest rates, this will reduce the purchasing power of the consumers.

In contrast to nominal interest rates, the real interest rates are calculated after considering inflation and therefore indicate the actual purchasing power of the consumers. And so, the real interest rate can be calculated as nominal interest rate less inflation rate, and this interest rate is measured by the consumer price index or CPI.

Effective interest rates are a compounded interest rates. Investors and borrowers must understand the difference between these interest rates.

**What is APY?**

Financial institutions (FI) such as banks accept deposits from the public and pay interest to them for the amount they borrow from the public. The financial institutions then lend this money to borrowers who would want money to run businesses or to buy assets such as houses, vehicles. The financial institutions charge interest from the borrowers, which is usually higher than the interest they pay the depositors.

The reward or benefit passed in the form of interest rate on to the depositors from a saving account or fixed deposits are known as the Annual Percentage Yield (APY). The APY uses the compounding interest method and therefore is always higher than the stated interest.

Formula to calculate APY is:

$$\text{APY}={\left(1+\frac{\text{i}}{\text{n}}\right)}^{\text{n}-1}$$

Where:

i = the stated annual interest rate

n = the number of compounding periods in one year

**Who or What determines the Interest Rates? **

The interest rate charged by banks or FI is determined by many factors such as current global situations, the current state of the economy, etc. In short, the supply and demand of money are some of the main factors that determine the interest rates. In this COVID-19 pandemic scenario, the mortgage rates dropped to a new low; emergency cuts in interest rates were announced globally. The rate cuts translated to cheaper mortgages meaning that people had to pay out less on their monthly payments on mortgages. The current mortgage rates are yet to recover, post the pandemic.

In the U.S., interest rates are determined by the Federal Open Market Committee (FOMC). In several other countries, the country’s Central Bank and the committee on monetary policy decisions the interest rates. These committees review and draw up monetary policies in different periods to manage inflation, maximize employment and stabilize the interest rate to promote the stability of the financial system of the country.

Generally, the interest rates are lower in developed countries than the under-developed and developing countries.

## Context and Application:

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for:

- Bachelor of Business Administration
- Bachelor of Commerce
- Master of Business Administration
- Master of Commerce
- Chartered Financial Analyst
- Chartered Accountant

### Want more help with your finance homework?

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

# Interest Rate Homework Questions from Fellow Students

Browse our recently answered Interest Rate homework questions.