Understanding Compounding Interest: Formulas and Examples

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Exploring the Formulas

Future Value Formula

The future value formula is used to calculate the value of an investment at a future date, taking into account the compounding interest. The formula is as follows:

  • FV = PV * (1 + r)^n

Where:

By plugging in the appropriate values for PV, r, and n, you can calculate the future value of an investment. This formula is useful for determining how much an investment will grow over time.

Present Value Formula

The present value formula is used to calculate the value of an investment at the present date, taking into account the compounding interest. The formula is as follows:

  • PV = FV / (1 + r)^n

Where:

  • PV is the present value of the investment
  • FV is the future value of the investment
  • r is the interest rate per period
  • n is the number of periods

By plugging in the appropriate values for FV, r, and n, you can calculate the present value of an investment. This formula is useful for determining the current worth of an investment.

Illustrating with Examples

Example 1: Savings Account

Suppose you have $10,000 that you want to invest in a savings account with an annual interest rate of 5%. The interest is compounded annually. Let’s see how your investment will grow over a period of 5 years.

Using the formula for compound interest, we can calculate the future value of your investment:

Future Value = Principal Amount × (1 + Interest Rate)^(Number of Compounding Periods)

For this example:

  • Principal Amount = $10,000
  • Interest Rate = 5% = 0.05
  • Number of Compounding Periods = 5 (years)

Future Value = $10,000 × (1 + 0.05)^5 = $12,762.82

So, after 5 years, your initial investment of $10,000 will grow to approximately $12,762.82.

Example 2: Dividend Stocks

Let’s consider another example with dividend stocks. Suppose you invest $5,000 in a dividend stock that pays an annual dividend yield of 3%. The dividends are reinvested back into the stock. You plan to hold the stock for 10 years. How much will your investment grow?

Using the formula for compound interest, we can calculate the future value of your investment:

Future Value = Principal Amount × (1 + Interest Rate)^(Number of Compounding Periods)

For this example:

  • Principal Amount = $5,000
  • Interest Rate = 3% = 0.03
  • Number of Compounding Periods = 10 (years)

Future Value = $5,000 × (1 + 0.03)^10 = $6,744.32

So, after 10 years, your initial investment of $5,000 will grow to approximately $6,744.32 due to the compounding effect of reinvesting dividends.