Jacqueline Strauss, a 25- year- old personal loan officer at Second National Bank, under-stands the importance of starting early when it comes to saving for retirement. She has committed $ 3,000 per year for her retirement fund and assumes that she’ll retire at age 65. a. How much will she have accumulated when she turns 65 if she invests in equities and earns 8 percent on average? b. Jacqueline is urging her friend, Mike Goodman, to start his plan right away, too, because he’s 35. What would his nest egg amount to if he invested in the same manner as Jacqueline and he, too, retires at age 65? Comment on your findings.
To calculate the amount Jacqueline will have accumulated when she turns 65, given an annual investment of $3,000 and an average return rate of 8 percent, we can use the future value of an ordinary annuity formula:
Future Value = Payment x [(1 + r) ^ n - 1] / r
Where:
Payment = $3,000 (the annual investment)
r = 8% (the average return rate, or 0.08 as a decimal)
n = 65 - 25 = 40 (the number of years Jacqueline will be investing)
a. Plugging in the values into the formula:
Future Value = $3,000 x [(1 + 0.08) ^ 40 - 1] / 0.08
Calculating this equation will give us the total amount Jacqueline will have accumulated when she turns 65.
b. For Mike Goodman, who is 35 years old, the number of years he will be investing is 30 (65 - 35). Using the same formula, we can calculate his potential nest egg:
Future Value = $3,000 x [(1 + 0.08) ^ 30 - 1] / 0.08
Comparing the future values of Jacqueline and Mike will provide insights on the impact of starting early on retirement savings.
Let's calculate these values now: