Interest is the compensation provided by the borrower to the lender for the usage of money, expressed as a percentage or sum. The notion of interest serves as the foundation for the majority of global financial products.

There are two techniques of accumulating interest: simple interest and compound interest.

Simple Interest

The following is a basic explanation of how interest works. Derek would like to borrow $100 (also known as the principle) from the bank for a year. The bank wants 10% interest on it. How to compute interest: $100 × 10% = $10

Derek owes the bank $110 a year later, $100 in principal and $10 in interest.

Assume Derek intended to borrow $100 for two years rather than one, and that the bank calculates interest on an annual basis. He would only be charged the interest rate twice, once at the end of each year.

Two years later, Derek owes the bank $120: $100 for the principal and $20 for interest.

The formula for calculating simple interest is:

Interest is calculated by multiplying the principal, interest rate, and term.

When applying interest at more sophisticated frequency, such as monthly or daily, use the following formula:

Interest is calculated by multiplying the principal by the interest rate, term, and frequency.

Compound Interest

Compounding interest takes more than one period, so let’s return to the example of Derek borrowing $100 from the bank for two years at a 10% interest rate. For the first year, interest is calculated as usual.

$100 × 10% = $10

This interest is applied to the principal, resulting in Derek’s current due repayment to the bank.

$100 + $10 = $110

However, the year finishes and a new time begins. Instead of using the original amount, compound interest is calculated using the principal plus any interest earned since then. In Derek’s case:

$110 × 10% = $11

Derek’s interest charge at the conclusion of year two is $11. This is added to the amount owed after year one:

$110 + $11 = $121

When the loan is paid off, the bank receives $121 from Derek rather than $120 if simple interest was used. This is because interest can be earned on interest.

The more frequently interest is compounded over a certain time period, the greater the interest generated on the original principal. The graph below depicts a $1,000 investment with various compounding frequencies producing 20% interest.

Initially, all frequencies are nearly identical, but they gradually begin to diverge over time. This is the power of compound interest that everyone loves to talk about, depicted in a succinct graph. The continuous compound will always yield the best return since it takes advantage of the mathematical limit on the frequency of compounding that can occur during a given time period.

The Rule of 72

Anyone who wants to calculate compound interest mentally may find the rule of 72 extremely beneficial. Not for precise calculations like those provided by financial calculators, but rather to generate general estimates. It asserts that to get the number of years (n) required to double a specific amount of money at any interest rate, simply divide 72 by that rate.

At 8% interest, it will take 9 years to turn $1,000 into $2,000. This method works best for interest rates ranging from 6 to 10%, although it should also work quite well for rates lower than 20%.

Fixed vs. Floating Interest Rate

The interest rate on a loan or savings can be “fixed” or “floating.”  Floating rate loans and savings are typically based on a reference rate, such as the Federal Reserve’s (Fed) funds rate or the London Interbank Offered Rate (LIBOR).  Typically, the loan rate is slightly higher, while the savings rate is slightly lower than the reference rate. The discrepancy is used to increase the bank’s profits.  Both the Fed rate and the LIBOR are short-term interbank interest rates, but the Fed rate is the primary weapon used by the Federal Reserve to control the availability of money in the US economy. LIBOR is a commercial rate determined from the current interest rates of highly creditworthy organizations. Our interest calculator only works with fixed interest rates.

Contributions

The Interest Calculator above allows for periodic deposits/contributions. This is handy for individuals who save a set amount on a regular basis. An essential distinction to note about contributions is whether they occur at the start or conclusion of the compounding period. Periodic payments made at the end result in one less interest period total per contribution.

Tax Rate

Bonds, savings, and certificate of deposits (CDs) are among the types of interest income that are taxable. In the United States, corporate bonds are almost always taxed. Certain types are fully taxed, while others are partially taxed. For example, while interest on U.S. federal treasury bonds is taxed at the federal level, it is normally excluded at the state and municipal levels. Taxes can have a significant impact on the final balance. For example, if Derek saves $100 at 6% for 20 years, he will receive:

$100 × (1 + 6%)20 = $320.71

This is tax-free. However, if Derek’s marginal tax rate is 25%, he will only receive $239.78 because the 25% tax rate applies to each compounding period.

Inflation Rate

Inflation is described as a steady rise in the prices of goods and services over time. As a result, a fixed quantity of money will allow you to spend less in the future. The average inflation rate in the United States over the last century has been roughly 3%. As a point of contrast, the S&P 500 (Standard & Poor’s) index in the United States has an average yearly return rate of roughly 10% for the same time period.

For quick, generic answers, use our Interest Calculator with an inflation rate of zero. However, for genuine and precise values, it is feasible to enter amounts that account for inflation.

Taxation and inflation combined make it difficult to increase the real value of money. For example, in the United States, the middle class has a marginal tax rate of roughly 25%, with an average inflation rate of 3%. To retain the value of the money, a consistent interest rate or investment return rate of 4% or above must be earned, which is difficult to attain.