Question

1. [3 points] Jason just accepted a job as an Operational Excellence Engineer with a local company. His starting salary is $74,000 per year. Jason plans to invest 8% of his annual salary each year in the Fidelity Growth Mutual Fund (consider this as a savings account earning 8% interest per year). Jason is also contracted to receive a 3% salary increase every year for the entirety of his employment. Jason plans to invest 8% of his annual salary in the mutual fund only for the next 35 years. If the mutual fund averages a 6% annual return over the 35 years: a. [1 point) How much will Jason have saved at the end of 35 years? Assume that his first deposit occurs at the end of the first year. b. [1 point] Jason's friend Ricardo is also interested in saving some of his salary but would prefer to save an equal amount each year, rather than increasing his annual investment over time. How much would Ricardo have to invest each year for the next 35 years, in order to have saved $20,000 more than Jason? C. (1 point) Serena, Jason's older sister only has 15 years left until her retirement. She just received a significant promotion at work which came with a large financial bonus. Because of her situation she knows that she can make the largest investment in the mutual fund at the end of the first year ($7,000) but will need to reduce her contribution by 2.5% each year thereafter. How much would Serena have saved by the end of her investment period?

Answer 1

1. Jason's Savings at the end of 35 years.

Future Value = C/(r-g) * {(1+r)ⁿ-(1+g)ⁿ}

Where,

C = Amount of initial investment = $ 5,920

r = Rate of return = 6%

g = Growth rate of investment = 3%

n = Term = Number of years = 35 years.

Future Value = 5920/(.06-.03) * {(1.06)³⁵-(1.03)³⁵}

Future Value = 197,333 * { 7.6861 - 2.8139 }

Future Value = 197,333 * 4.8722

Future Value = $ 961,452

Therefore, Jason's Savings at the end of 35 years would be $ 961,452.

2. Amount of Investment for Ricardo to save $ 20,000 more than Jason.

Future Value = P × (1+r)ⁿ−1)​/r

Where,

Future Value = Savings at the end of term = $ 961,452 + $ 20,000 = $ 981,452

r = Rate of return = 6%

n = Term = Number of years = 35 years.

Future Value = P × {(1+r)ⁿ−1}​/r

981452 = P * {(1.06)³⁵ - 1) / 0.06

981452 = P * { 7.6861 - 1) / 0.06

981452 = P * 111.43

P = $ 8807.41

Therefore, Ricardo will have to invest $ 8807.41 each year to save $ 20,000 more than Jason.

3. Serena's Savings at the end of 15 years.

Future Value = C/(r-g) * {(1+r)ⁿ-(1+g)ⁿ}

Where,

C = Amount of initial investment. = $ 7,000

r = Rate of return = 6%

g = Growth rate of investment = - 2.5%

n = Term = Number of years = 15 years.

Future Value = 7000/[.06-(-.025)] * {(1.06)¹⁵-(.975)¹⁵}

Future Value = 82,353 * { 2.3966 – 0.684 }

Future Value = 82,353 * 1.7125

Future Value = $ 141,033.

Therefore, Serena's Savings at the end of 15 years would be $ 141,033.