Question

John is not a regular investor. He has not bought or sold stock in the past year. His boker charged him an inactivity fee of $75. What type of fee is this?

Answer 1

John's inactivity fee is a service charge for a low-activity brokerage account. The example given of Alexx and Spenser's investments concerns compound interest calculations over 30 years, with and without a management fee.

Step-by-step explanation:

The inactivity fee that John's broker charged him is a type of service fee some brokerage firms impose on accounts that do not meet a minimum number of trades or account activity within a certain period. Generally, this fee compensates the brokerage firm for maintaining an account that is not generating transaction-based revenue.

The scenario with Alexx and Spenser relates to compound interest growth of investments over time, taking administrative fees into account. To calculate the future value of their respective investments, we would use the compound interest formula:

1. 
   
3. For Alexx: A = P(1 + r/n)^(nt), where P is the principal amount ($5000), r is the annual interest rate (0.05 for 5%), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
4. 
   
6. For Spenser: Adjust r to account for the management fee (0.0475 for 4.75%).

After 30 years of growth at these rates, the amount more that Alexx would have than Spenser can be calculated by subtracting the future value of Spenser's investment from that of Alexx's.