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Dr. sisters has been secretly depositing $10,500 in her savings account every december starting in 2000. her account earns 6 percent compounded annually. how much did she have in december 2021?

User Shuk
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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.

User Rizwan Jamal
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