I recently got into investing and I'm trying to calculate my ROI, it doesn't seem to go very well and I don't see my mistake.

I am interested in the mathematics of this question moreso than the actual result. This is about mathematics, not finance.

Ok so: Suppose I invested an initial sum $x(0)$ and I want to know $x(t)$ where $t$ stands for work days since initial investment. Each day my investment earns some profit, and that profit is then invested as well.

Suppose the investment grows at fixed percentage. Meaning $x(t) = x(t-1)+\alpha x(t-1)$ where $\alpha$ is some (hopefully positive) constant.

I managed to show that $x(t) = x(0)(1+\alpha)^t$ via simple induction.

From the definition we have $x(1) = x(0)(1+\alpha)$, now suppose $x(t-1) = x(0)(1+\alpha)^{t-1}$, which agrees with the $x(1)$ case. Then from the definition $x(t) = x(t-1)(1+\alpha)$ and applying the assumption we get $x(t) = x(0)(1+\alpha)^t$

Mathematically this makes sense and is fairly straightforward, but in real world scenarios it really doesn't seem to work out.

Suppose I invested $60000\$$ 5 days ago, and I noticed that each day I was earning roughly $0.03$ of the investment sum the previous day. For instance, $x(1) = 60020\$$ so $\alpha = 0.03$.

Following that logic, $x(5)$ which is where we are today, should be $67884\$$. Sadly for me, it is not. It is a substantially lower amount, much closer to $60000$.

Where is the mistake here?

  • $\begingroup$ Perhaps you have confused a percentage point of $1/100$th from a basis point of $1/10000$th? $60,000 * (1.03)^5$ is approximately $69600$ but $60,000 + (1.0003)^5$ is approximately $60090$. $\endgroup$ – Toby Mak May 28 '17 at 4:56
  • 1
    $\begingroup$ What is your calculation to get $\$67,884$ ? $\endgroup$ – callculus May 28 '17 at 4:56
  • $\begingroup$ The calculation is $x(5) = x(0)*(1+\alpha)^5 = 60000*(1.03)^5$ $\endgroup$ – Rick Joker May 28 '17 at 4:59
  • $\begingroup$ @RickJoker it's slightly off though it equals to 69556 $\endgroup$ – Yujie Zha May 28 '17 at 4:59
  • $\begingroup$ Your formula is correct: this is a simplified version of the compound interest (en.wikipedia.org/wiki/Compound_interest) formula where $n=1$. This version is commonly used in IGCSE and IB exams. How did you plug the variables into the formula? $\endgroup$ – Toby Mak May 28 '17 at 4:59

I think you messed up with $0.03$ v.s. $0.03 \%=0.0003$

Your equation is


And now you get $60020$ by setting $\alpha = 0.03 \%$

$$60020 \approx 60000 \times 1.0003$$

  • $\begingroup$ Oh... I see...Yes that's correct. Thank you. Careless mistake. $\endgroup$ – Rick Joker May 28 '17 at 4:59
  • $\begingroup$ You are welcome :) $\endgroup$ – Yujie Zha May 28 '17 at 5:01
  • $\begingroup$ @Yujie Zha Your answer looks very similar to my first comment. Did you copy it? $\endgroup$ – Toby Mak May 28 '17 at 5:02
  • $\begingroup$ @TobyMak Of course not. It took me a while to type, that's why I was 40-ish secs slower than your comment - if I see yours and type, I would not have been that fast :) $\endgroup$ – Yujie Zha May 28 '17 at 5:04
  • $\begingroup$ @Yujie Zha OK, perhaps this was just a coincidence. $\endgroup$ – Toby Mak May 28 '17 at 5:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.