What is Interest?

Interest is the cost of borrowing money or the reward for saving it. When you deposit money into a savings account, the bank pays you interest. Conversely, when you borrow money, you pay interest to the lender. Interest is typically expressed as an annual percentage rate (APR).

How Interest Grows

Interest grows over time, and its growth can be categorized into two main types: simple interest and compound interest.

Simple Interest is calculated only on the initial amount (principal). The formula is:

A = P (1 + r)^(t)

where:

• A is the amount of money accumulated after t years, including interest.
• P is the principal amount (the initial money).
• r is the annual interest rate (as a decimal).
• t is the time the money is invested for, in years.

Compound Interest is calculated on the principal amount and also on the accumulated interest of previous periods. The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:

• A is the amount of money accumulated after t years, including interest.
• P is the principal amount (the initial money).
• r is the annual interest rate (as a decimal).
• n is the number of times interest is compounded per year.
• t is the time the money is invested for, in years.

Compounding Interest

Compounding interest means that the interest is calculated on both the initial principal and the accumulated interest from previous periods. This causes the investment or loan balance to grow at an accelerating rate.

Compound Frequency refers to how often the interest is calculated and added to the principal balance. Common compounding frequencies include annually, semi-annually, quarterly, monthly, daily, etc. The more frequently interest is compounded, the more interest will be earned or paid.

Factors Affecting the Final Value

Several factors can influence the final value of an investment or loan:

• Starting Principal: The initial amount of money invested or borrowed. A larger starting principal will result in more interest earned or paid over time.
• Interest Rate: The percentage at which interest is calculated. Higher interest rates will increase the amount of interest earned or paid.
• Time (Years): The duration for which the money is invested or borrowed. More time allows for more interest to accumulate.
• Compound Frequency: The number of times interest is compounded per year. More frequent compounding periods (e.g., monthly vs. annually) result in more interest being earned or paid.
• Contributions: Additional deposits made into the investment. Regular contributions will increase the final value significantly due to the added principal and interest earned on these contributions.
• Withdrawals: Money taken out from the investment. Withdrawals reduce the principal, which in turn decreases the interest earned.

Examples

• Increasing Contributions: Regularly adding money to your investment will grow your balance more quickly, thanks to the interest earned on each new contribution.
• Making Withdrawals: Taking money out reduces the principal, which means future interest calculations are based on a smaller amount, resulting in less growth over time.
• Extending Time: Investing for a longer period allows for more compounding periods, which exponentially increases the final amount due to compound interest.
• Adjusting Interest Rates: Higher rates mean more interest earned on investments or more interest paid on loans.
• Changing Compound Frequency: More frequent compounding periods (e.g., monthly vs. annually) lead to faster growth of the investment.