Copyright

You want to have $30,000 in your savings account eight years from now, and you're prepared to...

Question:

You want to have $30,000 in your savings account eight years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 6.00 percent interest, what amount must you deposit each year?

Annuity Payments:

The annuity payments are the equal payments that one may invest over a period of time at a given rate of return to reach a target investment value in the future. These payments are directly related to the target value.

Answer and Explanation: 1


The amount that needs to be deposited each year is $3,031.08


The payments can be calculated from the future value of the annuity formula:

{eq}FV=P\times \dfrac{(1+r)^{n}-1}{r} {/eq}

Here:

  • Future value (FV) is the target sum = $96,463
  • P (Payment) is required
  • r (rate) = 6.00% or 0.06
  • n (Periods)= 8

Plugging in the values from the question, we have:

{eq}$30,000 = P \times \dfrac{(1+0.06)^{8}-1}{0.06}\\ $30,000 = P \times 9.897467909\\ P = \dfrac { $ 30,000 } { 9.897467909 }\\ P = $3,031.08 {/eq}


Learn more about this topic:

Loading...
How to Find the Value of an Annuity

from

Chapter 21 / Lesson 15
9.4K

An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.


Related to this Question

Explore our homework questions and answers library