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So I found this popular solution online (in the image above, below the question) and I was wondering why they chose this process.

I think I get the process for the solution above but does my attempt work as well?

My Attempt:

When I saw the problem I thought about calculating the Future Value of $$60,000 over 10 years @ 10% interest and comparing it to the Future Value of Annuity of a $10,000 payment over 10 years @ 10% interest.

I can show calculations, but isnt this method more straight forward?

mathguy
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  • Well, I don't understand why you would compute the future value of the annuity at all. Just get the present value, which is $10\times (d+ d+d^2+\cdots +d^{10})$ where $d$ is the discount factor $\frac 1{1.1}$. This works out to about $61.45K$ which is greater than $60K$. – lulu Oct 27 '17 at 23:49
  • They're equivalent. For the annuity, the work is the same. They divide that the future value of the annuity by $(1.1)^{10}$ and compare the result to $60$, whereas you multiply $60$ by $(1.1)^{10}$ and compare the result to the future value of the annuity. Same work. – quasi Oct 27 '17 at 23:51
  • @quasi I expect your reading is correct. I already edited my comment accordingly. – lulu Oct 27 '17 at 23:53
  • @mathguy: But lulu's suggested method is simpler still. – quasi Oct 27 '17 at 23:56
  • I was just thinking I could compare the future value of a lump sum with the future value of an annuity instead of finding the present value of annuity and comparing it with 60,000 – mathguy Oct 27 '17 at 23:56
  • How did you get the future value of the annuity? – quasi Oct 27 '17 at 23:58
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    Note: They didn't find the present value of the annuity. They found the present value of the future value of the annuity, and that is a lump sum. – quasi Oct 27 '17 at 23:59
  • i got the FVA = 10,000 ( (1.1)^10 - 1 ) / 0.1 ) – mathguy Oct 28 '17 at 00:01
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    Same as what they did, no? – quasi Oct 28 '17 at 00:01
  • Yes actually, but I guess I thought it was easier to calculate the FV of 60,000 instead of calculating the PV of the FVA – mathguy Oct 28 '17 at 00:04
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    Thus, your method of calculating FVA is identical to theirs. The took FVA, divided it by $(1.1)^{10}$ and compared it to $60$. One division, one comparison. You took $60$, multiplied it by $(1.1)^{10}$, and compared it to FVA. One multiplication, one comparison. – quasi Oct 28 '17 at 00:07
  • Let us continue this discussion in chat. – mathguy Oct 28 '17 at 01:49

1 Answers1

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As stated by @quasi

"your method of calculating FVA is identical to theirs. The took FVA, divided it by (1.1)10(1.1)10 and compared it to 6060. One division, one comparison. You took 6060, multiplied it by (1.1)10(1.1)10, and compared it to FVA. One multiplication, one comparison."

mathguy
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