My Math Forum Accumulated Future Value Help

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 December 11th, 2012, 06:59 PM #1 Newbie   Joined: Sep 2012 Posts: 22 Thanks: 0 Accumulated Future Value Help Okay so i'm having an issue. I'm trying to find the future value of this problem and I did it out by hand the exact way that my professor did in class, then to check I used this button on my calculator(don't know what exactly it is called but it's the button that puts in that fancy curved line where you put a number at the bottom and top of the line) that basically sets up the function and all i have to do is fill in the numbers. Problem is that the answer I get from doing it by hand is different from the one I get by plugging it into the calculator. Now I'm trusting the method my professor gave us but what has me skeptical is the fact that I used the previously mentioned button in a different type of problem before and the answer it gave me was the same as the one I got doing it out by hand, so i'm wondering why it is giving me a different answer this time around. Note that I've been doing this problem for about 30min now and I've made absolutely certain that I'm putting everything in right. The problem is this: You are granted a continuous income stream of $120,000 per year for 20 years. You invest the money at 8.2%, compounded continuously. Find the accumulated future value of the continuous income stream. I got 6080735.872 as an answer by doing the work by hand and my calculator got 12372406.83. As you can see there is a vast difference between these answers. I'm asking if someone on here can do the work by hand and tell me what they got as an answer and see if it matches the one I got by hand or the one my calculator got. This would be greatly appreciated!  December 11th, 2012, 09:49 PM #2 Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications Re: Accumulated Future Value Help If it is given (and I think that it is) that the$120,000 is accrued continuously, and the interest is compounded continuously, then I think that your calculation is correct. I get: $FV=pay $$(1+i)^{n-1}+(1+i)^{n-2}+...+(1+i)^{1}+1$$$ Since $\ x^{n-1}+x^{n-2}+...+x+1=\frac{x^n-1}{x-1} \$, $\ pay=\frac{120k}{\frac{n}{20}} \$, and $\ i=\frac{0.082}{\frac{n}{20}} \$ then $FV=\frac{120k}{\frac{n}{20}} \ \left( \frac{\left(1+\frac{0.082}{\frac{n}{20}}\right)^n-1}{\frac{0.082}{\frac{n}{20}}}\right) \$ (1) $FV=\frac{120k}{0.082} \ \left(\left(1+\frac{1.64}{n}\right)^n-1 \right) \$ and taking the limit as n goes to infinity gives: $\fbox{FV=\frac{120k}{0.082}\left(e^{1.64}-1 \right)=6080735.872}$ We can also do the following calculations using equation (1): Payment accrued and interest compounded: Yearly: $5614619 Monthly:$6038772 Daily: $6079347 Hourly:$6080674

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### find the accumulated future value continuous income stream that has been compounded continuously at 5.5%.

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