Question

You've been hired to analyze the retirement prospects of Tom and Jerri Strickland. It's been determined they'll need $2,750,000 at retirement, which occurs in 30 years and are anxious to start a savings program to meet this goal.

They expect to live in retirement for 35 years and anticipate an average (after-tax) investment rate of 7%. What level of savings, put away at the end of each year, will provide the Strickland's with their desired retirement fund?

1) -$29,113

2) -$68,884

3) -$27,208

4) -$67,787

Answer 1

The Stricklands need to save approximately $25,762.45 annually to achieve their retirement goal of $2,750,000 in 30 years based on a 7% investment rate, with the closest provided option being -$27,208 (option 3).

Step-by-step explanation:

To calculate the level of savings Tom and Jerri Strickland need to put away at the end of each year to meet their retirement goal, we use the future value of an annuity formula. Given an after-tax investment rate of 7% and the desired future sum of $2,750,000 over 30 years, we're looking to find the annuity payment (A). The future value of an annuity formula is FV = A * {[(1 + r)^n - 1] / r}, where FV is the future value, A is the annuity payment, r is the rate of return per period, and n is the number of periods. Substituting the values, we get 2,750,000 = A * {[(1 + 0.07)^30 - 1] / 0.07}. Solving for A gives us the annual savings needed.

Using the formula, we calculate: A = 2,750,000 / {[(1 + 0.07)^30 - 1] / 0.07}. This simplifies to A = 2,750,000 / 106.766. Thus, A = $25,762.45. This means the closest option available rounding to the nearest dollar is -$27,208.