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How to calculate this with a simple calculator.

$$\sum_{i=20}^n=59 0.1\cdot600\cdot1.04^{60-i} = \text{ ?}$$

I tried this but it's wrong. Can somebody please tell me where I made a mistake?

=0,1*600*1,04^(60-20)*(1-1,04^60-(59-20+1)/1-1,04)

With this I obtained 8577,91017 and apparently the right answer is 5929,59217958

Michael Hardy
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alison monroe
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  • Just so we're clear, all of your commas are the same as decimal points, correct? Also, what is $n$? – Noble Mushtak Apr 21 '16 at 16:47
  • \sum_{i=20}^{n=59} 0.16001.04^(60-i) = ? I mixed "," and "." my bad. The , is for decimal – alison monroe Apr 21 '16 at 16:56
  • Welcome to math stack exchange. Does the sum go from $i=20$ to $i=59$ ? If so, you should omit the $n$ to avoid confusion. – Peter Apr 21 '16 at 16:58
  • Hint : Compute the easier sum $$\sum_{i=1}^{40} 0.1\cdot600\cdot1.04^i$$ having the same value. You can even simplify that to $$60\sum_{i=1}^{40} 1.04^i$$ – Peter Apr 21 '16 at 17:00

1 Answers1

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Some of the notation is a bit off, but I believe what you want is

$$\sum_{i=20}^{59}0.1\cdot600\cdot1.04^{60-i}=60\sum_{k=1}^{40}1.04^k=60\left(1.04^{41}-1.04\over1.04-1 \right)={60\cdot1.04\over0.04}(1.04^{40}-1)=1560(1.04^{40}-1)$$

which indeed computes to the given right answer. The key is that as $i$ runs from $20$ up to $59$, $60-i$ runs from $40$ down to $1$.

Barry Cipra
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