Question

A partially completed pension spreadsheet showing the relationships among the elements that constitute Carney, Inc., defined benefit pension plan follows. Six years earlier, Carney revised its pension formula and recalculated benefits earned by employees in prior years using the more generous formula. The prior service cost created by the recalculation is being amortized at the rate of $5 million per year. At the end of 2018, the pension formula was amended again, creating an additional prior service cost of $40 million. The expected rate of return on assets and the actuary’s discount rate were 10%, and the average remaining service life of the active employee group is 10 years.

Answer 1

To determine how much more Alexx's investment will grow compared to Spenser's over 30 years, the future values for both investments are calculated using the compound interest formula, and then the difference is found by subtracting Spenser's future value from Alexx's.

Step-by-step explanation:

The question involves calculating the future value of two investments that are compounded annually but at different effective annual rates due to an administrative fee in one of the investments. To find out how much more Alexx will have compared to Spenser after 30 years, we can use the compound interest formula: FV = PV (1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

• For Alexx, who invests directly and earns an annual rate of 5%, the future value would be calculated as $5,000(1 + 0.05)^30.
• For Spenser, who uses a retirement fund with a 0.25% fee and earns 4.75% after fees, the future value would be calculated as $5,000(1 + 0.0475)^30.

After calculating both future values, we subtract Spenser's future value from Alexx's future value to determine the difference in their investment returns after 30 years.