Final answer:
To determine Dr. Sisters' savings by December 2021, we use the future value formula for an ordinary annuity with annual payments of $10,500 at a 6 percent interest rate compounded annually over 21 years.
Step-by-step explanation:
Dr. Sisters has been making annual deposits of $10,500 into a savings account with a 6 percent interest compounded annually starting from December 2000 until December 2021. To calculate the total amount accumulated by December 2021, we use the future value formula for a series of equal payments made at the end of each period (ordinary annuity):
Future Value = Pmt × { [(1 + r)ˣⁿ - 1] / r }
Where:
- Pmt is the annual payment ($10,500)
- r is the annual interest rate (0.06)
- n is the number of years (2021 - 2000 = 21 years)
The calculation would look like this:
Future Value = $10,500 × { [(1 + 0.06)²¹ - 1] / 0.06 }
After computing this, we can determine Dr. Sisters' total savings by December 2021 due to the power of compound interest.