Question

How would we solve this equation for r?

Answer 1

\[S = P(1+r)^{n}\]

Answer 2

\[\Rightarrow \frac{S}P = (1 + r)^n\]\[\Rightarrow \left(\frac{S}P\right)^{1/n} = 1 + r\]\[\Rightarrow r = \left(\frac{S}P\right)^{1/n}-1\]

Answer 3

Divide both sides by P, take the nth root of both sides, then subtract both sides by 1.

Answer 4

\[|_{1} \frac{ S }{ P } = (1+r)^{n}\]

I was thinking of taking the log of both sides but is this necessary?

Answer 5

oh wait lol I think I see what you guys are talking about

Answer 6

so you just took both sides to the 1/n power

\[(\frac{ S }{ P })^{\frac{ 1 }{ n }} = (1+r)^{n^{\frac{ 1 }{ n }}}\]

was just wondering if we could use logs to do this or was I just overthinking it.

Answer 7

You take logs when the quantity you're solving for is inside the exponent.

Answer 8

I see, thanks guys