Question

Pension data for Sterling Properties include the following: ($ in thousands) Service cost, 2024 $ 112 Projected benefit obligation, January 1, 2024 850 Plan assets (fair value), January 1, 2024 900 Prior service cost—AOCI (2024 amortization, $8) 80 Net loss—AOCI (2024 amortization, $1) 101 Interest rate, 6% Expected return on plan assets, 10% Actual return on plan assets, 11% Required: Assume Sterling Properties prepares its financial statements according to International Financial Reporting Standa

Answer 1

To determine how much more money Alexx will have compared to Spenser after 30 years, due to the 0.25% administrative fee charged by Spenser's retirement fund, we use the compound interest formula with their respective interest rates (5% for Alexx with no fee and 4.75% for Spenser with the fee).

Step-by-step explanation:

To calculate the difference in the amounts Alexx and Spenser will have after 30 years due to the impact of retirement fund fees, we will apply the formula for compound interest.

For Alexx, who is investing directly without any fees, the formula can be written as A = P(1 + r)^n, where P is the principal amount ($5000), r is the annual interest rate (5% or 0.05), and n is the number of years (30). For Spenser, who is investing through a retirement fund with a 0.25% fee, the effective annual interest rate becomes 4.75% or 0.0475. Therefore, Spenser's future value calculation will be similar but with the adjusted rate.

For Alexx:

Alexx's Future Value (FVA) = 5000(1 + 0.05)^30

For Spenser:

Spenser's Future Value (FVS) = 5000(1 + 0.0475)^30

To find out how much more Alexx will have than Spenser after 30 years, we subtract Spenser's Future Value from Alexx's Future Value:

Difference = FVA - FVS

We then perform the calculations using a calculator or software that allows for the input of these formulas to determine the exact monetary difference between the two investments.