Question

Darnell Johnson's employer contributes 47. of Darnell $ 38, 400 salary into his retirement plan. Additionally, the hospital matches the 1% of his salary that Darnell himself puts into his own plan. Find the future value in 10 years assumming (a) funds earn 5% compounded semiannually and (b) funds earn 8% compounded semiannually. (c) Then find the difference between the two. (Hint: Assume all contributions into the plan occur at the end of semiannual periods)

Answer 1

The future value of Darnell Johnson's retirement plan, assuming a 5% interest rate compounded semiannually, is approximately $27,697.16.

Step-by-step explanation:

To find the future value of Darnell Johnson's retirement plan, we need to calculate the total contributions made by his employer and himself, and then calculate the future value of those contributions compounded semiannually for 10 years.

a) First, we calculate the total contributions made by Darnell's employer, which is 47% of his $38,400 salary:

Employer contributions = 47% × $38,400 = $18,048

Next, we calculate the total contributions made by Darnell himself, which is 1% of his salary:

Darnell's contributions = 1% × $38,400 = $384

The total contributions made by both Darnell's employer and himself is $18,048 + $384 = $18,432.

To calculate the future value of these contributions, we can use the compound interest formula:

Future Value = P × (1 + r/n)^(n × t)

where P is the principal (the initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the principal is $18,432, the interest rate is 5% (0.05), the number of times the interest is compounded per year is 2 (semiannually), and the number of years is 10.

Plugging in these values, we get:

Future Value = $18,432 × (1 + 0.05/2)^(2 × 10) ≈ $27,697.16

Therefore, the future value of Darnell Johnson's retirement plan, assuming a 5% interest rate compounded semiannually, is approximately $27,697.16.