If you deposit $10,000 every year into an account, paying 5% compounded annually, how long will...

Question:

If you deposit $10,000 every year into an account, paying 5% compounded annually, how long will it take to accumulate $1,000,000?

Future value of an annuity:

An annuity is a series of equal cash flows. The future value of an annuity is computed on the basis of time value of money. An annuity may be paid at the beginning of a specified period or at the end. Therefore an annuity can be classified as an annuity due or ordinary annuity respectively.

Answer and Explanation:

  • {eq}FV \ of \ an \ ordinary \ annuity = Annuity * \dfrac{( (1 + r )^{n} - 1) }{ r} {/eq}
  • {eq}1,000,000 = 10,000 * \dfrac{( (1 + 0.05 )^{n} - 1) }{ 0.05} {/eq}
  • {eq}6 = 1.05^{n} {/eq}

Introduce logs to determine the value of n:

  • {eq}n = \dfrac{ log(6)}{log( 1.05)} {/eq}
  • {eq}n = 36.7238 {/eq}

Learn more about this topic:

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How to Find the Value of an Annuity

from Algebra II Textbook

Chapter 21 / Lesson 15
8.5K

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