Final Answer:
1) The value after 20 years of the retirement savings plan is $2,024,717 (Option c).
2) This is calculated by compounding quarterly with a 10% interest rate and $6,000 deposits every three months.
Step-by-step explanation:
1) To calculate the future value of the retirement savings plan, we use the compound interest formula. The formula is A = P(1 + r/n)^(nt), where:
- A is the future value of the investment/loan, including interest.
- P is the principal investment amount (the initial deposit or loan amount).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per unit t.
- t is the time the money is invested or borrowed for, in years.
2) In this scenario, the interest is compounded quarterly (n = 4) at a 10% annual interest rate (r = 0.10), and deposits of $6,000 are made at the start of every three months. The time period is 20 years (t = 20).