I have some trouble finding sense from the simple interest formula and compound interest formula.
I have look everywhere online, and they all agree that the simple interest formula is $I = prt$. Similarly, I see that the compound interest formula is $I = P(1+\frac rn)^{nt}$
Logically, the compound interest should work for a simple interest problem too.
Therefore, if we arbitrarily use a principal of 100, and a rate of 10% growth for two years, we will get the following formulas:
$I = 100(1.1)(2) = 100(1.1)(2)$
$I = (100)(1.1)^{(1)(2)} = 100(1.1)^2$
Clearly, the two formulas are different. I have come up with my own conclusion that the simple interest formula on the web is wrong, and it should be $i = pr^t$. Can anyone confirm/debunk this. Please tell me why I am wrong/right. Much appreciated
The difference between simple and compound interest is that for simple interest you only get interest on the original principal, not on the accumulated interest.
If you deposit $100$ for two years at $10\%$ per year, simple interest pays you $10$ each year and you wind up with $120$. The interest is $prt=100 \cdot 0.1 \cdot 2=20$
Compound interest will pay you $10$ at the end of the first year, giving a balance of $110$. The second year it will pay interest on the your new balance of $100$, netting you $11$ for a balance of $121$ at the end of the second year. Now the final value (which your formula has as I but should be $I+P$) is $100(1+0.1)^2=121$.