Question

What percentage of the fund's assets are used for administrative and operating costs (i.e. fee charged to investors annually that is a percentage of the assets they have in the fund)?

Answer 1

After 30 years, Alexx will have approximately $15,986.87 more than Spenser.

Step-by-step explanation:

The administrative fee charged by retirement funds each year is equal to 0.25% of the managed assets. In this case, Alexx and Spenser each invest $5,000 in the same stock, with Alexx earning 5% annually and Spenser earning 4.75% annually. After 30 years, the difference between the amount Alexx will have and the amount Spenser will have can be calculated by subtracting the accumulated fee charged to Spenser's retirement fund from the accumulated earnings of both investors.

To calculate this, we first find the accumulated earnings for Alexx and Spenser. Using the formula A = P(1 + r)^t, where A is the accumulated amount, P is the principal amount, r is the interest rate, and t is the time period, we get:

1. Alexx's accumulated earnings: A = $5,000 * (1 + 0.05)^{30} = $16,288.95
2. Spenser's accumulated earnings: A = $5,000 * (1 + 0.0475)^{30} = $15,761.55

Now, let's calculate the accumulated fee charged to Spenser's retirement fund. The fee is equal to 0.25% of the managed assets, so:

Accumulated fee = $5,000 * (0.0025)^{30} = $302.08

To find the difference between Alexx and Spenser, we subtract the accumulated fee charged to Spenser from Alexx's accumulated earnings:

Difference = $16,288.95 - $302.08 = $15,986.87

Therefore, after 30 years, Alexx will have approximately $15,986.87 more than Spenser.

Answer 2

The percentage of a fund's assets used for administrative and operating costs is equal to the administrative fee charged by the fund, which is usually a percentage of the total assets in the fund. This percentage can be calculated by dividing the administrative fee by the total assets and multiplying by 100.

Step-by-step explanation:

In this question, we are asked to calculate the percentage of a fund's assets that are used for administrative and operating costs. The question mentions that many retirement funds charge an administrative fee equal to 0.25% on managed assets. This means that 0.25% of the total assets in the fund are used for administrative and operating costs.

To calculate this in dollar terms, we need to multiply the fee rate by the total assets in the fund. For example, if the fund has $100,000 in assets, the administrative fee would be $250 (0.25% of $100,000).

To express this as a percentage of the total assets, we divide the administrative fee by the total assets and multiply by 100. So, for the previous example, the percentage would be 0.25%.