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Mr. Jones has deposited his life savings of $70,000 in a retirement income plan with a local...

Question:

Mr. Jones has deposited his life savings of {eq}\$70,000 {/eq} in a retirement income plan with a local bank. The bank pays {eq}10.75\% {/eq} per year, compounded annually, on such deposits. What is the maximum fixed amount Mr. Jones can withdraw at the end of each year and still have the funds last for {eq}15 {/eq} years?

Value of an Annuity:

An annuity is a fixed amount of money that can be deposited or withdrawn each period over a defined time frame. An ordinary annuity is one in which withdrawals are made at the end of each period. We can calculate the value of the annuity if we know the present value of the annuity, the interest rate, and the time frame over which the withdrawals are made. The value is calculated using formulas that take into account the time value of money.

Answer and Explanation: 1

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PV = $70,000

r =10.75%

n = 15 years


{eq}\begin{align*} \ PV_{OA} & = Annuity * \dfrac{(1 - (1 + r )^{-n}) }{ r} \\ 70,000& = Annuity *...

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How to Find the Value of an Annuity

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Chapter 21 / Lesson 15
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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.


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