Compounded INterest

[HeyArnold]

A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?

A) 16 = (1.02)^x/4
B) 2 = (1.02)^x
C) 16 = (1.08)^4x
D) 2 = (1.02)^x/4
E) 1/16 = (1.02)^4x

[spoiler]OA: B.... Is there a way to approach this problem without manipulating the Compound interest formula?[/spoiler]

[gmatboost]

You need to know that

Final = Initial*(1 + r/n)^(nt)
r = rate, n = compounding periods, t = years

Here, Final = Initial*(1 + 0.8/4)^(4t)
Final = Initial*(1.02)^(4t)

Since we want it to grow 16 times, plug in 16*Initial for Final
16*Initial = Initial*(1.02)^(4t)
16 = (1.02)^(4t)
This isn't a choice though

The ones that are clearly wrong once you have gotten this far: A, C, E

Look at the others and see what they have in common. They both have 2 on the left.
It looks like we will need to take the 4th root of both sides, since instead of 16 we see a 2, which is the 4th root of 16. This is okay because we have a 4 in the exponent on the right.

16^(1/4) = [(1.02)^(4t)]^(1/4)
[spoiler]2 = (1.02)^(4*1/4*t)
2 = (1.02)^(t)
[/spoiler]