Interest Rate on $1 Table Creator

Interest Rate on $1 Table Creator
Future Value (FV) : Columns
Periods (n) : Rows

How the Calculator Works:

  1. Future Value (FV) as Columns:

    • Specify how many columns you want in the table (up to 20).
    • Input the starting future value (FV), which represents the target amount you want $1 to grow into.
    • Choose the increment for each column. For example, if the starting FV is $3.00 and the increment is $0.70, the columns would display $3.00, $3.70, $4.40, etc.
  2. Periods (n) as Rows:

    • Specify how many rows you want in the table (up to 50).
    • Input the starting period (n), which represents the number of periods (usually years) the investment will grow.
    • Choose the increment for each row. For example, if the starting period is 10 and the increment is 1, the rows would display periods of 10, 11, 12, etc.
  3. Calculating Interest Rate (I): The interest rate needed to grow $1 to the specified future value over the given period is calculated using the formula:

    I=((FV$1)1n1)×100I = \left( \left( \frac{FV}{\$1} \right)^{\frac{1}{n}} – 1 \right) \times 100

    Where:

    • FVFV is the future value.
    • nn is the number of periods (typically years).
    • The result is multiplied by 100 to express the interest rate as a percentage.
  4. Generating the Table: The calculator generates a table where:

    • Each column represents a future value (FV).
    • Each row represents a period (n).
    • The table cells contain the interest rate (I%) required to grow $1 to the future value in that column over the period in that row.

Example:

Let’s say you want to calculate the interest rate to grow $1 into various future values over 10–15 periods:

  • Columns (Future Values):

    • Start with $3.00 and increase by $0.70 for each column.
    • This gives future values: $3.00, $3.70, $4.40.
  • Rows (Periods):

    • Start with period 10 and increment by 1 for each row.
    • This gives periods: 10, 11, 12, 13, 14, 15.

The table will calculate the interest rate needed to grow $1 into $3.00, $3.70, and $4.40 over 10–15 periods.

Sample Calculation:

For a future value (FV) of $3.00 and a period (n) of 10:

I=((3.001.00)1101)×100I = \left( \left( \frac{3.00}{1.00} \right)^{\frac{1}{10}} – 1 \right) \times 100I=(31101)×100I = \left( 3^{\frac{1}{10}} – 1 \right) \times 100I=(1.116121)×100=11.612%I = (1.11612 – 1) \times 100 = 11.612\%

So, the interest rate required to grow $1 to $3.00 over 10 years is 11.612%.

Advertisements