Question

fred invest $9000 in an account where the interest is compounded annually. Three years later the account balance is $10,493.22. what interest rate was being paid

Answer 1

To find the interest rate being paid, use the formula for compound interest and solve for the interest rate and we get 5.363%.

Step-by-step explanation:

To find the interest rate being paid, we can use the formula for compound interest:

Final Balance = Principal Amount × (1 + Interest Rate)^Number of Years

Plugging in the given values, $10,493.22 = $9000 × (1 + Interest Rate)^3

Next, divide both sides of the equation by $9000 to isolate the (1 + Interest Rate)^3 term, giving us:

1.16647 = (1 + Interest Rate)^3

Take the cube root of both sides to solve for the interest rate:

1 + Interest Rate = 1.16647^(1/3)

Simplifying, we find Interest Rate ≈ 1.05363 - 1

≈ 0.05363

Now, convert the decimal to a percentage by multiplying by 100:

Interest Rate ≈ 5.363%