Questions: An investment of 15000 grows to 22417 over six years. Find the interest rate on the account if the interest is compounded annually.

Solution Steps

To find the interest rate for an investment compounded annually, we can use the formula for compound interest:

\[ A = P(1 + r)^n \]

where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (initial investment).
• \( r \) is the annual interest rate (in decimal).
• \( n \) is the number of years the money is invested for.

Given \( A = 22417 \), \( P = 15000 \), and \( n = 6 \), we need to solve for \( r \).

Rearrange the formula to solve for \( r \):

\[ r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1 \]

We are given the following values for the investment:

• \( A = 22417 \) (the amount after 6 years)
• \( P = 15000 \) (the initial investment)
• \( n = 6 \) (the number of years)

The formula for compound interest is given by:

\[ A = P(1 + r)^n \]

We need to rearrange this formula to solve for the interest rate \( r \):

\[ r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1 \]

Substituting the known values into the rearranged formula:

\[ r = \left(\frac{22417}{15000}\right)^{\frac{1}{6}} - 1 \]

Calculating this gives:

\[ r \approx 0.06925438210560886 \]

To express the interest rate as a percentage, we multiply by 100:

\[ \text{interest rate} \approx 0.06925438210560886 \times 100 \approx 6.9254 \]

Final Answer