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2008-10-06
<p><font size="3">有一道SOA-FM/2的题,在下百思不得其解,请教各位:</font></p><p><font size="3">At time 0, Paul deposits P into a&nbsp; fund crediting interest at an effective annual interest rate of 8%. </font></p><p><font size="3">At the end of each years 6 through 20, Paul withdraws an amount sufficient to purchase an annuity-due of 100 per month for 10 years at a nominal interest of 12% compounded monthly. </font></p><p><font size="3">Immediately after the withdrawal at the end of year 20, the fund is zero. Calcudate P.</font></p><p><font size="3">A. 41,000&nbsp; &nbsp;B.42,000&nbsp;&nbsp; C.43,000&nbsp;&nbsp; D.44,000 E.45,000</font></p><p><font size="3">不大明白其第二段中的说法,自己作出来的数字相差甚远。</font></p><p></p><p>谢谢!!!</p>
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2008-10-6 10:55:00
<p>Answer is A.</p><p>解答中会用到100*a“two dot angle 120 at 0.01”=7039.76。</p>
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2008-10-6 11:23:00
<p>my answer is A. </p><p>Px1.08^6=&nbsp;Qx(1-1.08^-15)/d&nbsp; where</p><p>Q= 100* (1-1.01^-120)/0.01 and</p><p>d= i/(1+i)=0.08/1.08</p><p>so if you slove&nbsp;for&nbsp;P, it gives me $40604, so the closest answer is A.&nbsp;</p><p>my cal is only a rough one though, you may want to expand and elaborate it yourself.&nbsp; but the theory holds anyway. </p>
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