ontariodealer Joined: Aug 5, 2013
• Posts: 996
December 23rd, 2016 at 11:24:32 PM permalink
If a person invests \$1000 on aug 1 2015, then 1000 on the first of every month until dec 1, 2016 he has invested a total of \$17,000......on dec 31st he has \$17,600.

what is the r.o.i??????????
get second you pig
teliot Joined: Oct 19, 2009
• Posts: 2223
December 24th, 2016 at 6:35:06 AM permalink
I am not sure I understand what you mean by r.o.i. here. Assuming that interest accrues monthly, which you did not say, the interest the person is earning is approximately 0.3842% per month or 4.6104% per year.
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ThatDonGuy Joined: Jun 22, 2011
• Posts: 4926
December 24th, 2016 at 9:18:24 AM permalink
Going by a strict definition of ROI, you invested \$17,000 and got back \$17,600, so the ROI = profit / investment = 600 / 17,000 = 3/85 = about 3.5294%

There's no "quick formula" way to calculate the monthly rate of interest, as you get 17 months of interest on the first 1000, 16 on the second, 15 on the third, and so on, down to 1 for the 17th, so you get:

1000 (x17 + x16 + x15 + ... + x) = 17,600

x17 + x16 + x15 + ... + x - 17.6 = 0

where x is the monthly multiplier (e.g. for 1% monthly interest, x = 1.01).
There's no formula for solving a polynomial of degree 5 or higher; you have to use an approximation method like Newton-Raphson or Halley, both of which require at least some knowledge of calculus.
teliot Joined: Oct 19, 2009
• Posts: 2223
December 24th, 2016 at 10:53:50 AM permalink
Mr. Don, plugging your equation into Wolfram Alpha gives the same result I got in the spoiler above.

Copy and paste:
`x^17 + x^16 + x^15 +x^14 + x^13 + x^12 +x^11 + x^10 + x^9 +x^8 + x^7 + x^6 +  x^5 +x^4 + x^3 + x^2 + x - 17.6 = 0`

Into: https://www.wolframalpha.com/
Poetry website: www.totallydisconnected.com
MathExtremist Joined: Aug 31, 2010
• Posts: 6526
December 24th, 2016 at 11:11:36 AM permalink
ROI is just return divided by investment, so 600/17000 = 3.53%. If you want the IRR (internal rate of return) you can compute in a spreadsheet using the IRR function. Type in -1000 in 17 rows (negative representing outgoing cashflow, aka investment) and in the 18th row type 17600 (positive representing incoming cashflow, aka liquidation). Then compute the IRR over those 18 rows and you'll get the periodic rate of return which is 0.384%.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
ontariodealer Joined: Aug 5, 2013
• Posts: 996
December 24th, 2016 at 11:54:30 PM permalink
hey thanks guys, you are phenomenal
get second you pig
teliot Joined: Oct 19, 2009
• Posts: 2223
December 25th, 2016 at 3:44:55 PM permalink
Quote: MathExtremist

ROI is just return divided by investment, so 600/17000 = 3.53%. If you want the IRR (internal rate of return) you can compute in a spreadsheet using the IRR function. Type in -1000 in 17 rows (negative representing outgoing cashflow, aka investment) and in the 18th row type 17600 (positive representing incoming cashflow, aka liquidation). Then compute the IRR over those 18 rows and you'll get the periodic rate of return which is 0.384%.

Awesome. Excel continues to surprise me. I had to give it an initial guess ... =IRR(C3:C20,0.4%) = 0.38417091%
Poetry website: www.totallydisconnected.com
lilredrooster Joined: May 8, 2015