Case Title: Investing for Retirement $-$ The Time Value of Money in Action

Background: Sarah and John, both in their late $20$s$,$ are close friends who recently started working in

their respective fields. They have been discussing their financial goals and planning for the future. One of

their main concerns is preparing for retirement, even though it seems quite far away. They understand

the concept of the time value of money and its importance in financial planning.

Scenario: Sarah and John decide to put the time value of money into action by making different

investment choices for their retirement planning.

Sarah's Approach: Sarah decides to start investing early in a retirement fund. She starts investing $$5,000$

per year in a tax$-$advantaged retirement account at the age of $28.$ She plans to continue this annual

contribution for $10$ years, after which she will not contribute any more money. She will let her

investment grow over $30$ years using the compounding method.

Assumptions for Sarah's Investment:

Annual contribution: $$5,000$

Investment period: $10$ years $($from age $28$ to $38)$

Average annual return on investment: $7\%$

John's Approach: John believes that he has plenty of time to save for retirement later on$,$ so he delays

starting his retirement fund until he turns $38.$ At that point, he plans to invest $$5,000$ per year in the

same type of retirement account as Sarah. He intends to contribute for $30$ years until he retires.

Assumptions for John's Investment:

Annual contribution: $$5,000$

Investment period: $30$ years $($from age $38$ to $68)$

Average annual return on investment: $7\%$

Questions

What are the potential benefits of starting to invest for retirement at an early age?

Calculate the final investment balance for Sarah after $10$ years of contributing. How does Sarah's

investment strategy demonstrate the principle of the time value of money? How much money

she will make after $30$ years at the age of $68?$

Calculate the final investment balance for John after $30$ years of contributing. Compare the final

balances of Sarah and John. What factors contribute to the difference in their retirement

savings?

Discuss the potential disadvantages of delaying retirement contributions, as demonstrated by

John's approach.