This question is flawed... there's no right answer (it's ALMOST 21.6 though)... To solve you just use the equation: 50 x (1 + i)^2 + 50 x (1 + i) + 50 = 125 x (1 + i)^2 and solve for i turns out to be 21.525% ...
Can it be done this way? I've seen some similar questions solved this way: Cash flow Diagram: 125m ^ | 50m````A=50m |.........|.........| |.........|.........| ----------------- 0.......1.........n=2 P = A (P/A, i%, n) 175m = 50m (P/A, i%, 2) 3.5 = (P/A, i%, 2) And then use the Discrete Compounding Interest Table to find where it fits? And then use Linear Interpolation to find i ?
my bad... i edited this part m (shorthand for 1000) P = 125,000 + 50,000 = 175,000 P = A (P/A, i%, n) 175,000 = 50,000 (P/A, i%, 2) 3.5 = (P/A, i%, 2)
That's the thing. There are two problems. First is, they ask for a rate, not a yield. Perhaps it's simple interest. The OP can shed some light, if he has no idea what e is or how to figure continuous yield from a rate then it is probably simple interest. The other problem is, 25.5% is closer to the exact answer than 25.6. Perhaps there was an understanding of rounding up, but otherwise the answer of 25.6 is out of tolerance. Interestingly, 19.5% as a rate works. I still wonder if the first choice was supposed to be 19.5 instead of 15.5.
Yeah, 21.5 (e^(21.52. . .)) -1 = ~19.5% Whoops, that's backwrds. Too much crap going on. Reverse it: (e^(~19.5)) -1 = 21.52. . . Using a compounded continuously rate of 19.5%, you end up with $224,373.8732 taking $125k on day 1 and $224,364.1383 taking 3 payments of 50k. Less than $10 difference. Using a yield of 21.6% produces 224755.712 and 224635.0848 for a difference of ~$120. A yield of 21.5% produces a difference of ~$40.