Question

Debra is planning for her retirement 34 years from now. She plans to invest $5,700 per year for the first 7 years, $7,100 per year for the next 11 years, and $15,800 per year for the remaining 16 years. All of the investments will be made at the end of the year. If Debra can earn 10% annual return on her investments, what will her retirement fund amount to at the end of 34 years? (Round factor values to 5 decimal places, es. 1.25124 and final answer to 2 decimal places, eg.458,581.25.) Click here to view factor tables Amount of retirement fund

Answer 1

Debra's retirement fund will be computed by calculating the future value of annuities for each phase of her investment strategy. Using the formula for the future value of annuity and a 10% return rate, we will sum the future values of the three investment phases to find the total amount available at her retirement.

Step-by-step explanation:

To calculate Debra's retirement fund total, we need to examine her investment strategy over the 34-year period and apply the compound interest formula for each phase. The first phase is investing $5,700 per year for 7 years, the second phase is $7,100 per year for the next 11 years, and the third phase is $15,800 per year for the remaining 16 years. Using the given 10% annual return rate, we'll compute the future value of each series of investments and sum them up to get the total retirement fund.

To calculate the future value of an annuity (a series of equal payments made at regular intervals), the formula is: FV = Pmt * ((1 + r)^n - 1) / r, where FV represents the future value of the annuity, Pmt is the annual payment, r is the annual interest rate, and n is the number of payments. For each phase, we compound the payments for the remaining years to the retirement age. For instance, for the first series of payments, we compound it for 34-7=27 years. Summing the compounded values of all the payments for the three phases gives us Debra's retirement fund total.