. 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.
i = .08
n = 40 years
a) amount = 3000 ( 1.08^40 - 1)/.08
= appr $777,170.00
b) change the exponent from 40 to 30
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.
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a. To calculate how much Jacqueline will have accumulated when she turns 65, we can use the future value of an ordinary annuity formula. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Annual contribution
r = Interest rate per period
n = Number of periods
Given that Jacqueline invests $3,000 per year and the average interest rate is 8%, we can plug in these values into the formula:
FV = $3,000 * [(1 + 0.08)^40 - 1] / 0.08
Calculating this expression, Jacqueline will accumulate approximately $635,449.90 when she turns 65.
b. Now let's calculate how much Mike's nest egg would amount to if he starts at age 35. We use the same formula to calculate the future value:
FV = $3,000 * [(1 + 0.08)^30 - 1] / 0.08
Evaluating this expression, Mike would accumulate approximately $313,826.43 when he turns 65.
Commentary: By starting early and investing for a longer period of time, Jacqueline will accumulate a significantly larger nest egg than Mike, despite contributing the same amount per year and earning the same average interest rate. This is due to the power of compounding interest over time. Starting earlier allows more years for the investment to grow and earn additional returns. This demonstrates the benefits of early retirement planning and highlights the importance of starting as soon as possible to maximize retirement savings.