Regular semi-annual payments of 400 are deposited into an account paying 6.15% interest, compounded semi-annually. If the final value of the account is 46000 how long was the money invested? Select one: a. 24.17 years b. 24.96 years c. 26.84 years d. 25.33 years

## Step 1: Identify given information### We are given semi-annual payments 400 r = 6.15\% = 0.0615 FV = \ . We need to find the time in years.## Step 2: Determine the semi-annual interest rate and number of periods### Since the interest is compounded semi-annually, the semi-annual interest rate is . Let be the number of semi-annual periods. We are looking for in years, so .## Step 3: Apply the future value of an ordinary annuity formula### The future value of an ordinary annuity is given by the formula: . Substituting the given values, we have: .## Step 4: Solve for n### Simplify the equation: . Multiply both sides by 0.03075: . Add 1 to both sides: . Take the logarithm of both sides: . Solve for : .## Step 5: Calculate the time in years### Since represents the number of semi-annual periods, the time in years is years.