How do I calculate per year profit percentage if the profit percentage for 2 years is given?

Question

I am calculating the profit percentage per year. My investment for 2 years is \$2700 and my returns after two years is \$2815. So, the profit is \$115. The profit percentage is 4.25% for 1 year 10 months. How can I calculate yearly profit?

Answer 1

There is in my opinion not one way how to find such an answer. So here is just one way: Use monthly increments. You gained $4.25$% over a period of $22$ months. I assume compound interest principle, so if $g$ is the monthly growth factor, then we have $g^{22}=1.0425$. Now taking the $22$th root, we have the growth factor per month: $g=1.001893685$. Now if you want your hypothetical growth factor for $24$ months, you can simply do $g=1.001893685^{22}$ which is $1.04645$. Converting back to a percentage, this would be $4.645$%, slightly more than the $4.25$% based on $22$ months. If you want to know for ONE year: $g=1.001893685^{12}$ = $1.0229624$ which is approx $2.296$%

Answer 2

Assuming simple interest, divide the profit percentage for 22 months (1 year 10 months) by 22, then multiply by 12 to get the percentage per year.

4.25% / 22 X 12 is approx 2.32% (2 d.p.)

Check with the 2-year profit of $115:

115 / 2700 * 100 is approx 4.629% (3 d.p.), halved is approx 2.31% (2 d.p.)

I suspect the 4.25% figure may have been rounded to 2 decimal places, hence the discrepancy.

Answer 3

Compound interest is represented by the equation $A=P\left(1+\frac{r}{n}\right)^{nt} $ Where $A$ is the total interest earned, $r$ is the interest rate, $P$ is principal, $r$ is the interest rate, $t$ is the time (in years) and $n$ is the number of times per year interest is compounded.

If we assume your intrest is calculated on a daily basis, about $375$ times per year, we can fill in the equation:

$$115=2700\left(1+\frac{r}{365}\right)^{365\cdot2}$$ All we need to do now is simplify to solve for $r$.

$$115=2700\left(1+\frac{r}{365}\right)^{365\cdot2} \\ 115^{730}=2700\left(1+\frac{r^{730}}{365^{730}}\right) \\ 115^{730}=2700+\frac{2700r^{730}}{365^{730}} \\ 115=1.0108820811 + \frac{2700r}{365} \\ 41975 = 369.027428955 + 2700r \\ 41605.972572= 2700r \\ r \approx 15.4096$$