Math Question (r.o.i.)

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??????????

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.

Mr. Don, plugging your equation into Wolfram Alpha gives the same result I got in the spoiler above.

Copy and paste:

Into: https://www.wolframalpha.com/

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%.

hey thanks guys, you are phenomenal

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%

This threw me when I first started investing. I had an investment which I hadn't added to or withdrawn from in a couple of years. The first year the value of the investment lost 20%. The next year it gained 24%. When I saw the % gain for the 2nd year I thought I was ahead. But when I saw the dollar amount I realized I wasn't ahead. I was still down.