An employee starts working at the age of $22$ at an annual salary of $$50,000.$ She hopes to get an average increase of $3\%$ each year. Each year, her retirement plan requires her to contribute $8\%$ of her annual salary and the employer will contribute $35\%$ of her contribution, i$.$e$.,$ the employee contributes $$4000$ to the retirement fund in year $1$ and the employer contributes $$1400,$ making the balance a $$5400.$ The current balance in the retirement fund earns an annual return of $8\%$ which is applied into next year. This means the year $2$ balance is the year $1$ balance plus $8\%$ return on the year $1$ balance plus the year $2$ employee and employer contributions.

Develop an Excel model for retirement planning. Extend this model up to $65$ years of age

Type your answers to parts a$,$ b$,$ and c from your solution in the space provided below. Be brief and to the point.

Part a: How old will she be when the retirement balance grows to $$1$ million? What is the retirement balance at the age of $65?$

Part b: Suppose the yearly salary increase is not fixed at $3\%$ but randomly varies between $1$ to $5\%$ based on a uniform distribution. Which Excel function will you use to generate this yearly increase? In this scenario, how old she will be when the retirement balance grows to $$1$ million?

Part c: Keep the salary increase as uniformly random as in part b$.$ Now consider the scenario where the return on investment is not fixed at $8\%$ but randomly follows a normal distribution with a mean of $8\%$ and standard deviation of $1\%.$ Which Excel function will you use to generate this return on investment? In this scenario, how old she will be when the retirement balance grows to $$1$ million?

Must use Excel Formulas and Provide lots of screenshots on how to set it up and the formula in each.