You have accumulated some money for your retirement. You are going to withdraw $53975 every year...
Question:
You have accumulated some money for your retirement. You are going to withdraw $53975 every year at the end of the year for the next 30 years. How much money have you accumulated for your retirement? Your account pays you 10.54% per year, compounded annually. To answer this question, you have to find the present value of these cash flows. Round the answer to two decimal places.
PV of Annuity:
If cash flows are equal and occur at the end of each period for a specified amount of time, they form an ordinary annuity. The value of such series of cash flows can be computed using the formula for the present value of an ordinary annuity. The formula uses the interest rate (discount rate), the amount of payment and the number of periods to determine the present value of a fixed stream of payments.
Answer and Explanation: 1
Present value of cash flows that form an ordinary annuity can be determined through the following formula:
{eq}PVOA = PMT * \frac{1-(1+i)^{-n}}{i} {/eq}
where PVOA is the present value of an ordinary annuity, PMT is the periodic payment, i is the interest rate and n is the number of periods.
The annual payment (withdrawal) is $53975, and it will be made at the end of each year for the next 30 years. The interest rate is 10.54% per year with annual compounding. Thus:
{eq}PVOA = 53975 * \frac{1-(1+10.54\%)^{-30}}{10.54\%} = $486759.01 {/eq}
So, you have accumulated $486759.01 for your retirement.
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How to Calculate the Present Value of an Annuity
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Chapter 8 / Lesson 3
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Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.
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