<p>Funding your retirement You plan to retire in exactly 20 years. Your goal is
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<p>Funding your retirement You plan to retire in exactly 20 years. Your goal is to<br />create a <a id="KonaLink0" class="kLink" href="http://www.justanswer.com/homework/41qt9-funding-retirement-plan-retire-exactly-20-years.html"><span><span class="kLink">fund</span></span></a> that will allow you to receive $20,000 at the end of each year for<br />the 30 years between retirement and death (a psychic told you would die exactly<br />30 years after you retire). You know that you will be able to earn 11% per year<br />during the 30-year retirement period.<br />a. How large a fund will you need when you retire in 20 years to provide the<br />30-year, $20,000 retirement annuity?<br />b. How much will you need today as a single amount to provide the fund calculated<br />in part a if you earn only 9% per year during the 20 years preceding<br />retirement?<br />c. What effect would an increase in the rate you can earn both during and prior<br />to retirement have on the values found in parts a and b? Explain.<span><br /></span></p>Explanation / Answer
a) This is a present value of annuities problem. The formula for PV of annuity: PV = [C/i] * [1-1/{(1+i)^n}] Where C = annuity payments i = interest n = payment periods. PV = [$20,000/.11] * [1-1/{(1+.11)^30}] PV = $173,875.85 b. This will be a present value of principle problem. The formula for PV of principle: PV = P / [(1+i)^n] Where P is the amount you want after n years at i interest PV = $173,875.85 / [(1+.09)^20] PV = $31,024.82 c. If the interest in part a. went from .11 to .20, you'd need only $99,578.73. Likewise, in part b., if the .09 went to, say .15 and the interest from part a. remained at .11, you'd only need $10,623.86. This is because higher compounding interest rates will generate more money, meaning less would be needed today to get the same output tomorrow.
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